In his showdown Wednesday with BP's top executives, President Obama will demand that they turn over a "substantial" amount of money to an independent mediator who will handle claims from people and businesses harmed by the environmental disaster, administration officials said Sunday. 
 
 The White House wouldn't say how much money it wants BP to put in the new escrow account, but Senate Democrats named their number Sunday, sending a letter to BP asking it to create a $20 billion fund to handle economic damages and cleanup costs. 
 
 BP did not reject the demands out of hand, and it took pains to avoid anything resembling a confrontational posture as it prepares for Wednesday's session. 
 
 Behind the scenes, the situation is much tenser. The administration, under immense political pressure to show that it's fully in charge, is pressing BP to fully clean up the mess both environmentally and economically. BP, however, fears any plan going forward that would create a potentially unlimited liability. 
 
 Whether BP accedes to the administration's latest demands will probably depend on the precise details of the third-party mediator process -- and most critically on what specifically will be considered a legitimate claim against the company. 
 
 "We're looking forward to a very constructive discussion with the administration. We will want to explain what we're doing, but we'll also be very much in listening mode," BP spokesman Andrew Gowers said Sunday. 
 
 The company's position is that it will pay for claims directly associated with the oil in the gulf. The Obama administration, however, ratcheted up the potential scope of BP's liability last week when Interior Secretary Ken Salazar told Congress that the administration wants BP to pay for the lost wages of oil industry workers affected by the moratorium on deep-water drilling. White House press secretary Robert Gibbs, responding to questions from reporters, affirmed Salazar's position: "The moratorium is a result of the accident that BP caused. . . . Those are claims that BP should pay." 
 
 The comments triggered a one-day slide of 16 percent in BP's share price on Wednesday, alarming shareholders and company officials, who regard such a plan as a deal-breaker. The stickiest issues could be hashed out in private before the White House meeting, where Obama will go face to face with BP's controversial chief executive Tony Hayward and the little-seen chairman of the board, Carl-Henric Svanberg, among other BP executives. 
 
 "BP will not hand over a blank check to anyone, whether it's the administration or an independent mediator," said a person familiar with senior BP executives' thinking, speaking on the condition of anonymity because of the sensitivity of the negotiations. "BP will constructively engage in a process -- on the basis of transparent and pre-agreed rules -- a claims oversight process. That's a different matter." 
 
 This has become a transatlantic issue that has alarmed officials in the United Kingdom, where BP plays an outsize role in pension funds. Obama and British Prime Minister David Cameron spoke Saturday and agreed that the company must do all it can to respond to the spill, the White House said. 
 
 Obama will make his fourth trip to the gulf region Monday, then return to the capital for a Tuesday night address to the nation in which he is set to discuss the details of the escrow account, senior adviser David Axelrod said Sunday. 
 
 "We want to make sure that money is escrowed for the legitimate claims," Axelrod said on NBC's "Meet the Press." The president's discussion with BP executives will focus on the amount of money that should be set aside in the account, Axelrod said. ||||| WASHINGTON — Searching for a way to satisfy both the United States government and its own shareholders, the board of BP was examining three options for what to do with its next dividend, a person with direct knowledge of the board’s discussions said Monday. 
 
 The company’s $10.5 billion annual dividend has become a point of contention as President Obama has said BP should not be paying stockholders when fishermen, oil workers and small business owners are saying they cannot get the company to pay their loss claims from the oil spill in the Gulf of Mexico. 
 
 The discussions came as Mr. Obama headed to the Gulf Coast on Monday, his fourth trip to the region since the disaster struck, and as the company said that it would increase the amount of oil they would recover from the damaged well daily. 
 
 In answer to a request by the administration over the weekend that BP provide “a faster plan” to siphon off and collect the gushing oil, one with “greater redundancy and reliability,” the company said in a statement on Monday that it would move ahead with improvements to the system being used to siphon oil from the gushing well to boats on the surface, with the aim of increasing the amount of oil and gas it was collecting. 
 
 Mr. Obama’s trip to the Gulf Coast will be his first overnight visit since the April 20 rig explosion that caused the spill and, after three trips to Louisiana, his first tour of the states to the east — Mississippi, Alabama and Florida — that are in the direction of the spewing oil’s drift. With each trip, he has grown more critical of BP’s response, channeling the increasing anger and desperation of coastal residents and politicians. 
 
 The visit is part of a week of activities intended to convey presidential command of a crisis that continues to test both the government and BP, which said Monday that its costs of responding to the spill had risen to $1.6 billion. 
 
 On his return, Mr. Obama will speak to Americans from the Oval Office, a setting that past presidents have often used but which Mr. Obama never has, despite the gravity of the issues his administration has already faced, including the wars in Iraq and Afghanistan, the worst economic downturn since the Great Depression, and the president’s signature domestic initiative, overhauling the health care system. 
 
 Mr. Obama is expected to outline in his speech a plan to legally compel BP to create an escrow account to compensate businesses and individuals for their losses from the oil spill in the Gulf of Mexico, administration officials said on Sunday. 
 
 BP has said it does not expect to announce decisions about its dividend until after its chairman and chief executive speak with Mr. Obama at a meeting he has called for midweek. 
 
 “We are considering all these issues and look forward to constructive conversations on Wednesday in the White House,” said Andrew Gowers, a senior BP spokesman. 
 
 A person with direct knowledge of the board’s discussions said Monday that the board was considering three possible options: suspending payment of the dividend for two quarters, paying the dividend in bonus shares or escrowing the amount of the dividend while paying for the cleanup. Under the last option, BP would use cash generated from revenues to pay for the cleanup and would not tap the fund unless it was needed. This option, the person said, could offer some reassurance to both Washington and to shareholders that BP will pay for the cleanup while also trying to accommodate shareholders. 
 
 As critics continue to fault Mr. Obama less for his administration’s overall response to the spill than for what they say has been his own slow and reactive leadership style, the ultimatum to BP and the president’s use of the solemn setting of the Oval Office escalate his personal engagement to a new level. 
 
 On Sunday, the company used underwater robots to position sensors inside the well to measure how much oil is spilling, The Associated Press reported. 
 
 The robots were expected to insert the sensors through a line used to inject methanol, an antifreeze meant to prevent the buildup of icy slush, into the containment cap over the ruptured pipe, said a BP spokesman, David Nicholas. The work should be completed by Tuesday. 
 
 The actions set for this week reflect the administration’s efforts, nearly two months into the crisis, to telegraph a take-charge decisiveness when Mr. Obama and the federal government are all but powerless to actually resolve the calamity, given the sheer technological challenge of plugging a leak a mile below the gulf’s surface. Mr. Obama’s moves this week, together with events in Congress, put BP on the defensive more than at any other time since the explosion. 
 
 The administration has said that while BP alone has the technological capability to stop the leak, it must take direction from Adm. Thad W. Allen of the Coast Guard, Mr. Obama’s designated chief of the federal response, and other senior administration officials. 
 
 The president’s meeting on Wednesday will be his first face-to-face contact with top company officials, after weeks of questions about why he has not done so before. BP has notified the White House that, as requested, the chairman of BP’s board, Carl-Henric Svanberg, will come. He will bring along the company’s embattled chief executive, Tony Hayward, who has been much criticized for statements that have been considered insensitive and self-serving. 
 
 Mr. Hayward will be in the hot seat on Thursday as well, testifying before one of several Congressional committees investigating the spill. 
 
 Although a containment cap has apparently reduced the amount of oil surging from the gulf floor, BP will face questions about last week’s determination from government scientists that the volume of spilled oil has been as high as 40,000 barrels a day — many times higher than BP ever acknowledged. Admiral Allen said on CBS’s “Face the Nation” on Sunday that the “mid-30,000 range is what we’re looking at.” 
 
 The installation of the sensors on Sunday was done at the request of the team of scientists, according to The A.P.
– In his first-ever Oval Office speech tomorrow night, President Obama will demand that BP hand over billions of dollars to an independent mediator who will handle the claims of people and businesses affected by the Gulf oil spill. The White House hasn't named a sum, but House Dems asked BP for $20 billion for the escrow fund yesterday. The speech will come amid a week of activities that the president hopes will convince the public he's in control of the oil spill crisis, the New York Times reports. Those the administration wants BP to compensate include all oil industry workers affected by the current moratorium on drilling. The oil giant fears the plan would create unlimited liability for it, the Washington Post reports. Another current sore point as both sides gear up for Obama's meeting with BP leaders Wednesday is the $10.5 billion dividend BP had planned to pay out to shareholders, likely unfeasible in the current political environment. Topping off the week's confrontations with the government, BP head Tony Hayward will go before a congressional committee Thursday.