The White House has denied Mr Trump made such a request.
Thursday night, President Trump told NBC's Lester Holt he planned to fire Comey before his Deputy Attorney General, Rod Rosenstein, recommended it.
In a statement, Durbin said that what he characterized as Trump's admission that he fired Comey because of the Russian Federation probe was "dangerously close to obstruction of justice".
Spicer did not answer to questions whether the White House taped the conversation between Trump and Comey.
One week after Trump was sworn is as the 45th president of the United States, he met with Comey at a private dinner and asked the Federal Bureau of Investigation director to pledge his loyalty, according to a report by The New York Times.
Tim Cook testing Apple's non-invasive glucose tracker prototype
The source on the Apple campus told CNBC that Cook is indeed wearing a device and confirmed that it was an Apple prototype. Smith said developing such a device has been "the most hard technical challenge I have encountered in my career".
The deputy attorney general's memo cited Comey's news conference last July about the Clinton investigation, raising a "why now?" question about the dismissal.
White House spokeswoman Sarah Huckabee Sanders attributed the disconnect in the week's explanations to the fact that she had not directly asked President Trump when he'd made the decision to fire Comey until shortly before Thursday's press briefing.
"As a very active President with lots of things happening, it is not possible for my surrogates to stand at podium with flawless accuracy!"
Trump suggested they might be replaced with written responses "for the sake of accuracy".
The White House has consistently denied having links with Russian Federation.
Real Madrid sets its sights on first Liga title in 5 years
"Our form in La Liga is not good, and now after the defeat against Manchester United [in the Europa League] we must change this and concentrate".
Democrats are demanding appointment of a special prosecutor to investigate Russia's involvement in the 2016 election and ties to Trump's campaign, and have discussed trying to slow down the confirmation process or other business of the Senate as a way of drawing attention to the demand. He said the discussions happened in two phone calls and at a dinner in which Comey was asking to keep his job.
The president said he "had dealings over the years", including the Miss Universe pageant and the sale of a home to "a very wealthy Russian".
Comey had angered Democrats over his handling of the probe of Democratic presidential candidate Hillary Clinton's use of a private email server while she was secretary of state.
Acting FBIDirector Andrew McCabe, Republican Senator John Cornyn, New York Appeals Court Judge Michael Garcia and former Assistant Attorney General Alice Fisher will be interviewed on Saturday for the post, an administration official said. That's true at any time, and even more so when the FBI is investigating alleged collusion between the Russians and people associated with the Trump campaign.
"If Russia or anybody else is trying to interfere with our elections, I think it's a frightful thing and I want to get to the bottom of it and I want to make sure it will never ever happen", he said. Their review also notably takes into account only Trump's returns from the past 10 years, leaving open questions about whether there were financial dealings with Russian Federation in earlier years.
Si Woo Kim FedExCup standings update
World No. 1 Dustin Johnson carded a 68 in the final round, just his third round in the 60s in 30 career rounds at TPC Sawgrass. Rafa Cabrera Bello hit 8-iron that bounded off the side of a bunker and into the cup for an albatross 2 on the par-5 16th.