Washington (CNN) Rex Tillerson was sworn in as the Trump administration's secretary of state Wednesday evening after having been confirmed by the Senate earlier in the day.

"It's time to bring a clear-eyed focus to foreign affairs," President Donald Trump said at a White House ceremony, adding, "All of us are better off when we act in concert and not conflict. There's rarely been conflict in the world like we see today. Very sad."

Vice President Mike Pence gave the oath of office to Tillerson.

The former ExxonMobil CEO -- who was confirmed in the Senate by a vote of 56 to 43, with all Republicans in support and most Democrats voting against him -- fills one more slot on Trump's national security team despite questions about his approach to Russia and state sponsors of terror, such as Iran.

Three Democratic senators split with their party to back Tillerson: Joe Manchin of West Virginia, Heidi Heitkamp of North Dakota and Mark Warner of Virginia. They were joined by Independent Sen. Angus King of Maine, who caucuses with Democrats.

Sen. Bob Corker, a Tennessee Republican and chairman of the Senate Foreign Relations Committee, said he was sure Tillerson would be an effective leader at the State Department.

"Mr. Tillerson led a global enterprise with 75,000 employees, possesses deep relationships around the world, and understands the critical role of US leadership," Corker said in a statement. "He has expressed a commitment to defend American values and to restore US credibility by strengthening old alliances and building new ones."

Time of uncertainty

Tillerson will take the helm of the US government's oldest executive agency, founded in 1789, at a time when Trump has roiled some of America's oldest and most stalwart allies.

The European Union president warned Tuesday that the Trump administration now poses a "threat" after the President's declaration that NATO is "obsolete. Trump also has repeatedly praised Brexit and said he expects other countries to leave the EU.

Asian allies such as South Korea and Japan are seeking reassurance after Trump suggested reconsidering security ties.

On Wednesday, former CIA Director David Petraeus hammered home the message that the US' alliances are a crucial part of its national security.

"Americans should not take the current international order for granted," Petraeus said told the House Armed Services Committee. "It did not will itself into existence. We created it. Likewise, it is not naturally self-sustaining. We have sustained it. If we stop doing so, it will fray and, eventually collapse. This is precisely what some of our adversaries seek to encourage," he said, mentioning Russia in particular.

The 64-year-old Texan had a shaky confirmation hearing before Corker's committee in January, generating frustration among Democrats and Republicans alike after he dodged a series of questions. He wouldn't agree when asked if Russia's Vladimir Putin -- who has given Tillerson Russia's highest civilian honor for his work there as an oil man -- is a war criminal. Tillerson also avoided condemning human rights abuses in China, Saudi Arabia and the Philippines. And he sidestepped a direct answer about whether humans cause climate change.

Democrats also raised concerns about how long Tillerson would recuse himself from decisions that could affect ExxonMobil once he became the top US diplomat.

Sen. Chris Murphy, a Democrat from Connecticut, opposed Tillerson's nomination, questioning whether the Texan's close business dealings with Moscow would impact his response to any Russian aggression and arguing that "it is not the same thing to run a global business and run the State Department."

"We have reason to fear that Mr. Tillerson would run the State Department like he ran Exxon, where he repeatedly worked against US national interests," Murphy said Tuesday.

He noted that Tillerson opposed sanctions against Russia after its invasion of Ukraine and "was awarded the Order of Friendship by Vladimir Putin," Murphy said on the Senate floor. "We have a President who has openly mocked human rights, who has supported vicious dictators, and a secretary of state who has made a career of doing business with some of the worst human rights violators in the world."

Sen. Diane Feinstein, a California Democrat, said she voted against Tillerson because he claimed not to know about Exxon's history of lobbying Congress in opposition to sanctions on Iran and Russia. She cited public documents that show Exxon established a joint venture with Shell called Infineum. That venture's purpose was to conduct business with Iran, Sudan and Syria, all considered by the US to be state sponsors of terror and under US sanctions.

"During that time, Mr. Tillerson rose from senior vice president to president and director, and eventually to chairman and CEO of Exxon," Feinstein said. "Yet, during his testimony, Mr. Tillerson claimed to be unaware of Infineum's purposeful evasion of sanctions."

Eventually, Tillerson narrowly won approval from the Senate Foreign Relations Committee in a 10-11 vote along party lines.

Democrats had hoped to delay a final vote in order to quiz Tillerson about the Trump administration's travel ban on seven Muslim-majority countries. In his confirmation hearing, Tillerson said, "I do not support targeting any particular group."

Tillerson split from Trump on a series of issues in his confirmation hearing last month, condemning Russia's invasion of Ukraine as "illegal" and saying he did not oppose the Trans-Pacific Partnership trade deal that President Donald Trump has rejected.

Tillerson also pushed back against Trump's campaign suggestion that South Korea and Japan should consider developing nuclear arsenals. And unlike Trump, who has repeatedly questioned the utility of NATO and its members' financial contributions, Tillerson expressed clear support for the alliance.

CORRECTION: This story has been updated to correctly attribute Sen. Chris Murphy's remarks.