WASHINGTON (Reuters) - President-elect Donald Trump named the head of Exxon Mobil Corp, Rex Tillerson, as his choice for U.S. secretary of state on Tuesday and won backing from some Republican foreign policy figures ahead of a possible Senate fight over the oilman’s ties to Russia. The Exxon chief executive potentially faces difficulties getting confirmed in the Republican-controlled Senate. Some lawmakers worry about his links to Moscow and opposition to U.S. sanctions on Russia, which awarded him a friendship medal in 2013.     But several Republican establishment figures, including former Secretaries of State James Baker and Condoleezza Rice, and former Defense Secretary Robert Gates vouched for Tillerson, 64, who has spent more than 40 years at the oil company.  Rice and Gates, who have worked for Exxon as consultants, both issued statements of support on Tuesday.      Their backing could be crucial for Tillerson receiving the approval he needs in the Senate, where Republicans will have a slim majority when Trump takes office on Jan 20.     “The fact that Condi Rice, James Baker and Bob Gates are recommending Tillerson carries considerable weight,” said Republican Senator Jeff Flake, a member of the Senate Foreign Relations Committee. By choosing Tillerson, Trump adds another person to his Cabinet and circle of advisers who may favor a soft line toward Moscow, which is under U.S. sanctions for its 2014 annexation of Crimea and at the center of allegations that it launched cyber attacks to disrupt the U.S. presidential election.  Republican foreign policy hawks in the Senate like John McCain and Lindsey Graham are likely to give Tillerson a rough time at a confirmation hearing in early January. “It’s very well known that he has a very close relationship with (Russian President) Vladimir Putin,” said McCain, the Republican party’s 2008 nominee for president.   Republicans will have a majority of just 52-48 in the Senate, and only a few defections from their ranks would block Tillerson if every Democrat also opposed him.     Trump, on a victory tour of states that backed him in the November election, told supporters in West Allis, Wisconsin, that Tillerson “will be a fierce advocate for American interests around the world.” He called him “a strong man, a tough man.” Trump upset U.S. allies during his campaign by calling for a better relationship with Russia and questioning the usefulness of the North Atlantic Treaty Organization, the U.S.-led military bloc created after World War Two to counter the Soviet Union.  Trump has also pledged to confront China on trade and territorial issues and temporarily ban Muslims from entering the United States, angering many Islamic countries. Tillerson has foreign experience from years of cutting deals with foreign countries for his company, the world’s largest energy firm. In 2012, Tillerson signed a deal with Russian state oil giant Rosneft to jointly develop oil fields in western Siberia. He has been chief executive of Exxon Mobil since 2006     but like Trump he has never held public office. Tillerson said in a statement that he shared the president-elect’s “vision for restoring the credibility of the United States.” Exxon Mobil said its board would meet soon regarding its transition. Trump was also poised to add another figure with close ties to the oil industry to his Cabinet. A source close to the transition said Trump had chosen former Texas Governor Rick Perry, whose state is a leading oil producer, as his nominee for energy secretary, with an announcement expected soon.  Perry met Trump at Trump Tower in New York on Monday, part of a series of meetings that included rapper Kanye West on Tuesday. Trump also has offered the position of interior secretary to Montana first-term Representative Ryan Zinke, an ex-Navy SEAL commander who was an early Trump supporter, according to media reports. Trump appointed Stephen Miller, a top policy aide during the campaign, to be his senior adviser for policy. Miller had been an adviser to U.S. Senator Jeff Sessions of Alabama, whom Trump has nominated to be attorney general. In 2013, Putin bestowed a Russian state honor, the Order of Friendship, on Tillerson, citing his work “strengthening cooperation in the energy sector.” There also has been controversy over alleged Russian interference in the Nov. 8 presidential election, with the CIA concluding that Moscow had intervened to help Trump defeat Democrat Hillary Clinton. Tillerson’s “cozy ties to Vladimir Putin and Russia would represent an untenable conflict at the State Department,” Representative Eliot Engel, the ranking Democrat on the House of Representatives Committee on Foreign Affairs, said in a statement. Russian Foreign Minister Sergei Lavrov said Trump and Tillerson were “pragmatic people” who could help America and Russia build a mutually beneficial relationship.   A group of U.S. state attorneys general is investigating Exxon for allegedly misleading the public about climate change and some environmental groups are alarmed Exxon’s CEO could be America’s top diplomat. Exxon has said it has acknowledged the reality of climate change for years. Tillerson told a congressional hearing in 2010 he thought humanity contributed to climate change but the science was unclear about the size of the contribution. “It is extremely complicated,” he told the hearing. After Trump’s election, Exxon came out in support of the Paris Climate Agreement to combat climate change.        There also are concerns among lawmakers about former U.N. Ambassador John Bolton, who an adviser to Trump’s transition team said was still under consideration for the deputy secretary of state role.     Bolton has urged Washington to do more to counter China’s assertiveness in East Asia. 