WASHINGTON— Exxon Mobil Corp. Chief Executive Rex Tillerson, the top choice for secretary of state in a Trump administration, faces bipartisan resistance in Congress over his ties to Russian President Vladimir Putin.

GOP hesitation over Mr. Tillerson marked the first sign of division between congressional Republicans and the Trump team over its likely cabinet picks. All of President-elect Donald Trump’s other nominees so far appear likely to be confirmed by the Senate.

Mr. Tillerson, a seasoned deal-maker whose company has a long history of doing business in Russia, is drawing unease from senators on both sides of the aisle. Republicans can likely afford to lose only two GOP votes next year in the new Congress when it meets to consider Mr. Trump’s nominees.

“It’s a matter of concern to me that he has such a close personal relationship with Vladimir Putin,” Sen. John McCain (R., Ariz.) said Sunday on CBS , noting that the two men had done “enormous deals” together. “That would color his approach to Vladimir Putin and the Russian threat.”

Sen. Ben Cardin of Maryland, the top Democrat on the Foreign Relations Committee, the panel that would hold confirmation hearings on the nomination, said Sunday on CNN that he was “concerned about his [Mr. Tillerson’s] relationship with Russia. We want to make sure that the secretary of state is a person who represents America.”