Exxon Mobil Chief Executive Rex Tillerson is President-elect Donald Trump's choice as secretary of state, his transition team announced early Tuesday, but he could face a struggle getting confirmed by U.S. senators concerned about his close ties to Russia.

Trump called Republican Mitt Romney, another candidate for the top diplomatic job, to tell him he would not get it, a Bloomberg reporter tweeted Monday night.

Lawmakers from both major parties have raised questions about Tillerson and former U.N. Ambassador John Bolton, who has been mentioned as a possible No. 2 State Department official and has voiced hawkish views on Iraq and Iran.

Republicans and Democrats said Tillerson, who is also president of Exxon Mobil Corp, would be asked about his ties to Russia, having met President Vladimir Putin several times. He won fresh praise from Moscow on Monday.

In 2013, Putin bestowed a Russian state honor, the Order of Friendship, on Tillerson, citing his work "strengthening cooperation in the energy sector."

Sen. John McCain, a leading foreign policy voice and 2008 Republican candidate for president, told Reuters in an interview: "I have concerns. It's very well known that he has a very close relationship with Vladimir Putin."

Calling Putin "a KGB agent who is bent on restoring the Russian Empire," McCain said he would await confirmation hearings if Tillerson is nominated before making a judgment on the nomination.

Another Republican, Senator Marco Rubio, who serves on the Senate Foreign Relations Committee that would review a Tillerson nomination, has voiced similar worries.

Renewed allegations of Russian hackers meddling in the Nov. 8 election, coupled with Trump's stated admiration of Putin, have stoked concern. Washington is at odds with Moscow over a range of issues that include Syria, Ukraine and NATO's presence in Eastern Europe.

Trump, a Republican, is due to succeed Democratic President Barack Obama on Jan. 20. During Trump's presidential campaign, Democrats and longtime government officials voiced alarm when Trump repeatedly praised Putin.

BOLTON ALSO A CONCERN

Republican Senate Majority Leader Mitch McConnell said he was optimistic Trump's nominees would be confirmed by the Senate, but he declined to comment on any future nominees such as Tillerson.

McConnell called all of Trump's choices so far "pretty impressive."

Senator Charles Schumer, the incoming Senate Democratic leader, told CBS "This Morning" that "the bottom line is, every one of these nominees, particularly a guy like Tillerson, needs a thorough, thorough hearing."

"Talks about his closeness with Putin will come forward," Schumer said.

Bolton has also generated bipartisan concern. On Sunday, Republican Senator Rand Paul said he would work to stop Bolton from being confirmed to any Trump administration post.

"His worldview is naive," Paul said on ABC's "This Week." "He still believes in regime change. He's still a big cheerleader for the Iraq war. He's promoted a nuclear attack by Israel on Iran. He wants to do regime change in Iran."

In 2005, then-President George W. Bush installed Bolton as U.S. ambassador to the United Nations in a temporary "recess appointment" that sidestepped U.S. Senate confirmation. He took that step after Democrats used procedural rules in place at the time to block the nomination.

Bolton left the job at the end of 2006 when the temporary appointment was ending.

Senate rules have since changed, making it harder for a minority of senators to stop judicial and executive branch nominations. Republicans will hold a 52-48 majority in the Senate session that begins on Jan. 3.