“I don’t do cover-ups,” the Republican president said in an unscheduled briefing from the White House.
His remarks came after House Speaker Nancy Pelosi met fellow Democrats to discuss impeaching the president.
Mr Trump is fighting congressional inquiries by ignoring subpoenas, withholding documents and blocking testimony by current and ex-advisers.
What did President Trump say?
The president spoke minutes after cutting short a planned meeting with the two top Democratic leaders on Capitol Hill.
The trio were due to discuss spending on ageing US roads and bridges, a rare possible area of agreement between the White House and its political antagonists.
But Mr Trump abruptly left the discussion with House of Representatives leader Mrs Pelosi and her Senate counterpart Chuck Schumer after barely five minutes.
The president then appeared in the Rose Garden to make a surprise statement, condemning “phoney investigations” by Democrats.
Mr Trump also charged his political opponents with “abuse” and railed against their invoking of “the big i word” – impeachment.
How did Democrats respond?
Mrs Pelosi did not back down, later specifically mentioning the US constitutional process for removing a president from office.
She said at an event in Washington: “The fact is, in plain sight in the public domain, this president is obstructing justice and he’s engaged in a cover-up – and that could be an impeachable offence.”
At a press conference earlier with Mrs Pelosi, Mr Schumer accused Mr Trump of “running away”.
“When we got in the room, the curtains were closed,” the New York senator said about their brief meeting.
“There was a place for him at the front so he could stand and attempt to tell us why he wouldn’t do infrastructure, and of course, then he went to the Rose Garden with prepared signs that had been printed long before our meeting.”
After the Mueller investigation concluded, Donald Trump and his advocates cheered what they saw as a cloud over the White House finally lifting.
It turns out, however, the political weather is still gloomy. Congressional Democrats have picked up the mantle of the inquiry, issuing a flurry of subpoenas.
Now Mr Trump, in what was clearly a pre-planned response, is pushing back.
Co-operation and investigation, the president asserts, are mutually exclusive. Hopes of a legislative infrastructure deal have been dashed. Of greater immediate concern, however, is the status of negotiations on approving a new spending plan and raising the debt ceiling.
If Republicans in Congress follow the president’s lead and dig in their heels, a new round of budget crises could be on the way.
An infrastructure plan appeared to be the best way for the president and Democrats to enact substantive legislation that they could take credit for on the 2020 campaign trail.
If the current course continues, however, the two sides will instead be fighting over who should shoulder the most blame.
What’s behind this latest row?
Democrats on Capitol Hill have launched a number of oversight inquiries into Mr Trump, stemming from a special counsel report into alleged Russian meddling in the 2016 US presidential election.
Robert Mueller’s investigation did not establish any conspiracy between the Trump campaign and Kremlin, but listed repeated instances of possible obstruction of justice by the president.
On Wednesday alone, the president’s political foes stepped closer towards obtaining his closely guarded accounts.
A New York judge ruled that the president’s financial records could be provided to Democratic lawmakers by Deutsche Bank and Capital One bank.
And New York’s Democratic-controlled state legislature approved a bill designed to unseal the president’s tax returns, which he has repeatedly prevaricated about disclosing.
Earlier this week, a federal judge ruled that Mr Trump could not block a subpoena ordering his accounting firm to turn over his financial records to Congress.
On Monday, meanwhile, Mr Trump directed his former White House counsel Don McGahn to ignore a summons to testify to the House Judiciary Committee.
The panel responded by issuing subpoenas to two former White House staff members, including ex-communications director Hope Hicks.
Is there any chance of impeachment?
As Mr Trump stonewalls congressional investigations, Mrs Pelosi has been trying to tamp down increasing clamour among her fellow Democrats for impeachment proceedings.
On Wednesday, she met members of her party in a closed-door session and argued the time was not right for impeaching the president.
It was as she emerged from this caucus meeting that Mrs Pelosi angered the president by suggesting to reporters that he was involved in a cover-up.
The House leader has also said she believes the president is “goading” Democrats into pushing for impeachment.
A freshman Democratic congresswoman, Katie Hill, told the Associated Press after Wednesday’s meeting that impeachment was “becoming an inevitability” with every act of defiance from the president.
Impeachment would need to be approved a majority in the Democratic-controlled House, but it would stand virtually no chance of passing the Republican-controlled Senate.
Only two other presidents have been impeached: Andrew Johnson and Bill Clinton.