Donald Trump reportedly pressed James Comey to declare his "loyalty" just seven days after being sworn in as President, but the FBI chief refused.
Mr Comey, sensationally fired by the President earlier this week, said he could only offer "honesty".
According to sources quoted by the New York Times, the pair eventually settled on "honest loyalty" after Mr Trump pressed Mr Comey a second time.
The exchange is said to have taken place during a dinner meeting to which Mr Comey was summoned early in the Trump presidency.
Mr Trump claimed in an interview with NBC News that it was Mr Comey who requested the meeting because he wanted to keep his job, which NBC said sources close to the investigator denied.
He said: "He wanted to have dinner because he wanted to stay on. We had a very nice dinner at the White House."
It was also at the dinner that Mr Trump said the FBI director informed him he was not personally under investigation over his campaign's alleged ties to Russia.
The White House denied the New York Times' account.
Sarah Huckabee Sanders, the deputy press secretary, said: "The integrity of our law enforcement agencies and their leadership is of the utmost importance to President Trump. He would never even suggest the expectation of personal loyalty, only loyalty to our country and its great people."
