Buzzfeed has defended its explosive report alleging Donald Trump directed his then-personal lawyer Michael Cohen to lie to Congress about a Moscow real estate deal.

Reporter Anthony Cormier and editor-in-chief Ben Smith defended the story, insisting their sources are "solid" and their story is accurate despite prompting a rare response from Special Counsel Robert Mueller.

On Thursday, Buzzfeed published the story, written by Cormier and colleague Jason Leopold, alleging that Trump told Cohen to lie to Congress about a Trump Tower project in Moscow. The President has repeatedly denied having any business dealings with the Russians.

The story drew significant national and global attention, as it appeared to be the most direct allegation yet that Trump had obstructed justice.

Trump reportedly directed Michael Cohen to lie to Congress. Photo / AP

Some analysts pointed out that similar charges had led to the impeachment of President Bill Clinton and the resignation of President Richard Nixon.

Mueller's office released a rare statement following the article's release, disputing what was reported.

"BuzzFeed's description of specific statements to the Special Counsel's Office, and characterisation of documents and testimony obtained by this office, regarding Michael Cohen's Congressional testimony are not accurate," wrote special counsel spokesman Peter Carr.

Trump later went on a Twitter rant, claiming he was being treated worse than any other president since Abraham Lincoln and that the media was losing credibility.

But the journalists have defended the story in the face of mounting pressure, insisting it's accurate and that their sources — who have not been identified — are correct.

"I'm solid. My sources are solid," Cormier told CNN's Reliable Sources host Brian Stelter. "This is going to be borne out, Brian. This story is accurate."

He also said he has received "further confirmation" from the same two sources that the story is accurate, but repeatedly refused to offer any information about who the sources were.

When asked about the possibility that the sources are wrong, Cormier said: "They're not. I'm confident. Our standards on this story were extremely high."

Smith said he encouraged Mueller's office to clarify which statements they believed were "not accurate", saying: "We are eager to understand which characterisations Mueller is talking about and obviously we take that incredibly seriously. We haven't heard where the gap is and where we can continue our reporting to close it."

Stelter also asked the reporters whether they could be sure about the exact phrasing of the interaction between Trump and Cohen, and whether or not he specifically told him to "lie" — a matter that could prove crucial in determining the accuracy of the story.

"What really happened? Is it that Trump said to Cohen, 'Take care of me. Don't screw me.' Was it mob talk? It wasn't directing him to lie — it was telling him, 'Don't screw this up Michael'?"

Cormier said: "We don't know. We're trying to get the exact language that was used in this conversation, and we'll get there one day. We continue to report like mad, as we always do, but what we reported — that the President directed Michael Cohen to lie to Congress — is fundamentally accurate. We're going to get inside the room where it happened and bear it out."

Likewise, when asked why they published with only two sources, the reporters said: "We were very, very confident in the sourcing of this story. It's been developing over a long period of time, with a series of sources who were involved in these huge revelations."

BuzzFeed reporter @a_cormier_ on his story: “I have further confirmation that this is right. We are being told to stand our ground … The same sources that we used in that story are standing behind it, as are we.” https://t.co/rejBGLYLqC pic.twitter.com/Oe3yz5G0Dk

— Reliable Sources (@ReliableSources) January 20, 2019

Stelter also criticised the "shockingly casual" emails sent by co-author Jason Leopold to the Special Counsel's office requesting comment.

The email, addressed to Carr, said: "Peter, Hope all is well. Anthony and I have a story coming stating that Michael Cohen was directed by President Trump himself to lie to Congress about his negotiations related to the Trump Moscow project. Assume no comment from you but just wanted to check. Best, Jason."

"Do you think that was an appropriate and sufficient way to ask for comment?" Stelter asked the reporters.

"I know (Carr) has said that he wished had the email come in more formal with more detail, that he would have responded in more detail," Smith said. "We would love to have gotten more detail from him."

"But come on, one paragraph? That's a dereliction of duty," fired back Stelter.

"Mr Carr is a lovely spokesperson," replied Cormier. "We know him. We've dealt with him in the past on numerous occasions. It's never been my experience to get any kind of signal, wave-off, go-ahead through the special counsel's office through that spokesperson."

The reporters also said Buzzfeed was "prepared to defend itself" if there were any legal challenges.

Donald Trump slammed the report, claiming he was being treated worse than any other president since Abraham Lincoln and that the media was losing credibility. Photo / AP

If either Cormier or Smith are fearful their jobs may be on the line, they're not showing it. Asked about the prospect of getting fired and risking Buzzfeed's reputation, they said: "We're confident in the story and we think that while there is right now, understandably, a focus on the media story and the process, the important story here is the relationship between Trump and Russia.

"Our reporting is central to that and will continue to be."

Trump's current lawyer Rudy Giuliani left open the possibility that the President and Mr Cohen might have discussed his congressional testimony.

But he added, "so what" if he did?

Giuliani appeared on CNN overnight, where he said he did not know if Trump had discussed the congressional interview with Cohen.

He also acknowledged in a separate interview with NBC that conversations about that project stretched throughout 2016, including possibly up until October or November of that year.

On CNN he acknowledged the possibility that Trump and Cohen might have discussed Cohen's testimony, saying that while he had no knowledge of such a conversation, he wasn't ruling it out.

"I don't know if it happened or didn't happen," Giuliani said. "And so what if he talked to him about it?"

Trump's lawyer Rudy Giuliani left open the possibility that the President and Cohen might have discussed his congressional testimony. Photo / Getty Images

Giuliani's suggestion to NBC that dialogue about the Trump Tower project could have stretched into October or November 2016 extends the timeline well beyond what the President has publicly acknowledged.

Cohen pleaded guilty to lying to Congress by saying that he had abandoned the project in January 2016 even though prosecutors say he actually continued pursuing it into June. Giuliani said on NBC's Meet The Press that Trump could recall having conversations with Cohen about the project throughout 2016, though there "weren't a lot of them".

"The President also remembers — yeah, probably up — could be up to as far as October, November," Giuliani said. "Our answers cover until the election. So anytime during that period they could've talked about it. But the President's recollection of it is that the thing had petered out quite a bit."

Giuliani made a similar comment last month on ABC News when he suggested that the President knew that Mr Cohen was pursuing the project into 2016.

"According to the answer that he gave, it would have covered all the way up to — covered up to November, 2016. Said he had conversations with him but the President didn't hide this," Giuliani said.

— with AP