(CNN)A Saudi-led coalition Tuesday ended its "Operation Decisive Storm" -- its nearly monthlong airstrike campaign in Yemen -- and a new initiative is underway. "Operation Renewal of Hope" will focus on the political process. Saudi Arabia had launched airstrikes on Houthi positions across Yemen, hoping to wipe out the Iranian-allied rebel group that has overthrown the government and seized power. The Saudis say they want to restore the Yemeni government, a key U.S. ally in the fight against al Qaeda, which was kicked out of the capital by the rebels earlier this year. This month, Saudi officials said airstrikes have degraded Houthi-controlled military infrastructure, including key buildings in the capital Sanaa. The campaign achieved its objectives "by a very good planning, very precise execution, by the courage of our pilots, our sailors, our soldiers," said Brig. Gen. Ahmed Asiri, a Saudi military spokesman. A senior Saudi official told CNN that the Houthis agreed to "nearly all demands" of the U.N. Security Council. Former Yemeni President Ali Abdullah Saleh and his family will leave Yemen and never return for a position in politics, the source said. A statement from the Saudi Embassy in Washington outlined objectives of the next phase of operations, including protecting civilians, enhancing humanitarian and medical assistance, confronting terrorism and creating an international coalition to provide maritime security. Ground troops will continue to protect the border and confront any attempts to destabilize the situation, Asiri said. Military action will be taken if needed. But beyond the military campaign, the Saudis and their allies have said they want to find a political solution for the violence-plagued nation. The aim is to bring back Yemen's "security and stability through establishing a political process," said a statement from Saudi Arabia, the United Arab Emirates, Bahrain, Qatar and Kuwait. Ousted Yemen President Abdu Rabu Mansour Hadi thanked the Saudi-led coalition. Hadi claims he's Yemen's legitimate leader and is working with the Saudis and other allies to return to his country. "We promise to restructure the Yemen military to ensure that it serves the people of Yemen," Hadi said, calling on the Houthis to withdraw, and saying that he would return to Yemen at "the right time" to rebuild the country. "You will witness many changes in the days to come in our mission to build an institutional government and military, far from rebel militancy," said Hadi. Also Tuesday, a U.S. military official told CNN that the United States is conducting "manned reconnaissance" off Yemen. The official stressed that the repositioning of U.S. ships over the last days was not done to interdict Iranian ships, but to ensure freedom of navigation and maritime security. Why is Saudi Arabia bombing Yemen? CNN's Jethro Mullen, Tim Lister, Anas Hamdan, Jamie Crawford and journalist Hakim Almasmari contributed to this report.
Former Yemeni President Ali Abdullah Saleh will leave, a source says .
Ousted leader Abdu Rabu Mansour Hadi promises to return .
Next phase, called "Operation Renewal of Hope," will focus on political process .