Comey also said that he believed the president had fired him because of the Russian Federation probe, told "lies" about his record at the bureau and sought to redirect the probe away from former national security adviser Michael Flynn.
"I will tell you I didn't say that", Trump said at a conference in the White House Rose Garden.
Mr Comey also has said Mr Sessions did not respond when he complained he did not "want to get time alone with the President again". When asked if the former Federal Bureau of Investigation director was lying then, the president said, "Well, I didn't say that".
Collins said that she supported issuing a subpoena to obtain the tapes if they exist, but noted that it would probably come from special counsel Robert Mueller, who is leading an independent investigation into Trump and Russian Federation, rather than from the Senate intelligence panel.
"I hardly know the man [Mr Comey]", he said. "Who would ask a man to pledge allegiance under oath?"
Asked by Karl whether he would be willing to say these things under oath, Trump replied, "100 percent".
The Russia questions are likely to make headlines again on Tuesday as the USA attorney general, Jeff Sessions, said late Saturday that he would appear before the Senate intelligence committee as it investigates Russian meddling in the presidential election.
Comey has accusedTrump of firing him to derail an investigation into Russian interference in usa elections and then lying about the motives for the move.
The president also said Comey confirmed a lot of what Trump had claimed about their interactions, though he says other parts of Comey's testimony "just weren't true".
"First, I was alone with the. president-elect", Comey said of why he took notes.
TRUMP: Remember how nice you used to be before I ran?
Later Friday, Trump declined to rule out his previous claim that there may be tapes of his conversations with Comey.
Later in the day, White House adviser Kellyanne Conway refused to comment on whether a recording existed, or not.
He testified Thursday he didn't think about the possibility of their talks being recorded until Trump tweeted about it after his firing, "James Comey better hope that there are no "tapes" of our conversations before he starts leaking to the press!" I'm not hinting at anything...
Trump admin amends travel ban date to keep legal battle alive
He says the president was within his lawful authority to enact the temporary ban on visitors from six Muslim-majority nations. They also ruled that the travel ban would break immigration law which outlaws discrimination on the grounds of nationality.
12 dead in London high rise fire
Mike Penning, a member of British Parliament who is a former firefighter, said "cladding was clearly spreading the fire". A local residents association had previously warned it was anxious about the risk of a serious fire in the block.
Landslides kill 43 in Bangladesh after heavy rain
At least 10 more army men were injured, five critically, in the Rangamati incident, according to a press statement by the ISPR. The deaths in devastating landslides triggered by heavy rains in southeast Bangladesh rose to 125, an official said today.
Healthcare push may need more cash
In May, House Republicans narrowly passed Trump's health care bill that aims to repeal and replace key provisions of Obamacare. Senate Republicans are winnowing down policy options in search of 51 votes to advance House-passed legislation this summer.