US President Donald Trump repeatedly complained to FBI director James Comey in early 2017 that the Russia meddling investigation was a cloud over his young administration, weeks before firing him, leaked memorandums showed on Thursday.

Trump "said he was trying to run the country and the cloud of this Russia business was making that difficult", Comey wrote in a memo on a conversation they had on March 30, 2017.

Eleven days later, Trump again pressed Comey about the issue. The president told Comey that "he is trying to do work for the country, visit with foreign leaders, and any cloud, even a little cloud, gets in the way of that", Comey wrote, referring to "the Russia thing".

The memos, which Comey wrote immediately after several meetings with Trump in the weeks after his inauguration on January 20, 2017, depict a president deeply worried about the impact of the probe into Russian meddling in the election the previous year.

Obtained by AFP on Thursday after the Justice Department released them to Congress, the memos could become evidence in a criminal investigation into whether Trump consciously tried to obstruct the probe.

Comey makes clear in his memos that he was uncomfortable with the pressure and that it was not completely proper, though at the time he did not allege the president had broken any laws. But Comey never committed to easing off the investigation, which continues to examine a number of suspicious contacts between the Trump campaign and Russia.

Weeks after their last conversation, on May 9, Trump fired Comey, saying in an interview two days later that he decided to dismiss the FBI chief in part out of unhappiness over the Russia probe.

"In fact, when I decided to just do it, I said to myself, you know, this thing with Trump and Russia is a made-up story, an excuse by the Democrats for having lost an election."

"In my opinion, it should've been over with a long time ago."

Much of what is in the memos, most notably Trump's demand that Comey pledge his loyalty, has been known for nearly a year.

Comey wrote that the president repeatedly raised the still-unconfirmed story that Russians have a video of him with prostitutes in a Moscow hotel.

"The president said 'this hookers thing' is nonsense," Comey wrote. However, Trump also said "that Putin had told him, 'We have some of the most beautiful hookers in the world'," Comey noted.