The Washington Post first reported Wednesday that Mueller's probe was widening to include looking into whether Trump obstructed justice.
The letter said the investigation will also probe Comey's testimony that Loretta Lynch, as President Barack Obama's attorney general, had directed him to describe an FBI probe into Hillary Clinton's email practices as merely a "matter" and to avoid calling it an investigation. He declined further comment.
It was six days ago that Mr. Trump proclaimed that he had been vindicated by the Congressional testimony of former FBI Director James Comey, who said he had told the President several times that he was not under investigation related to Russian election interference.
A spokesman for Trump's attorney Marc Kasowitz fiercely denied the allegations.
"I was honestly concerned that he might lie about the nature of our meeting, and so I thought it really important to document", Comey said.
"Oftentimes what happens, frankly, in counterintelligence investigations is you start looking at sort of a core intelligence question - What did the Russians do and did they do it with any Americans? - and it grows into: What did any of those Americans do in their financial matters that may also raise alarms with the FBI?".
Mueller is overseeing a host of investigations involving people who are or were in Trump's orbit, people familiar with the probe were quoted as saying.
Trump appears to confirm obstruction investigation on Twitter
US President Donald Trump listens during a cabinet meeting at the White House in Washington , DC, on June 12, 2017. But Rosenstein, too, may ultimately have to hand off oversight given his role in Trump's decision to fire Comey .
The investigation into obstruction of justice "began days after Comey was sacked on May 9", The Washington Post story notes.
Trump's legal team quickly denounced the report on Wednesday.
Sooner or later, the RNC is going to realize that there are lots of other Republicans who aren't Donald Trump and would actually like to be reelected, but for now, they seem happy to implode their entire party with him. "Nice", the President tweeted.
These two file photos show US President Donald Trump (TOP) meeting with leaders of the pharmaceutical industry in the Roosevelt Room of the White House on January 31, 2017 in Washington, DC.
"I don't think it's for me to say whether the conversation I had with the President was an effort to obstruct", Comey said.
Asked by Senate Intelligence Committee Chairman Richard Burr at the June 8 hearing if Comey thought that Trump's actions amounted to obstruction, Comey said it wasn't his place to answer that question, and dropped a not-so-subtle hint that he expected questions of obstruction to be part of Mueller's investigation.
However, any findings of criminal activity would put pressure on the Republican-controlled Congress to use them as the basis for launching impeachment proceedings against Trump.
As part of the probe, the special counsel has also gathered Comey's written accounts of his conversations with Trump.