Mueller said there was no hard evidence of collusion, even if links between the real estate tycoon's campaign and Moscow did raise eyebrows.
At a press conference earlier with Mrs Pelosi, Mr Schumer accused Mr Trump of "running away".
"I don't do cover-ups".
"But you know what we can't do it under these circumstances", Trump said. But the meeting ended abruptly in "high drama", Senator Dick Durbin said, after Trump walked in and announced he wouldn't meet with them due to the ongoing investigations.
"Senate Minority leader Chuck Schumer claimed the president's storm-out was a setup and he never meant to negotiate over infrasctructure spending in the first place", the Mail said.
"He came into the room".
Later, in remarks to the Center for American Progress, Pelosi said: "This is why I think the president was so steamed off this morning: Because the fat is in plain sight, in the public domain, this president is obstructing justice and he's engaged in a cover up".
Across the aisle, House Speaker Pelosi told reporters that Amash's tweet "speaks volumes about the absence of any sound from the Republicans on the unethical behavior of the Trump administration". "And I just saw that Nancy Pelosi, just before our meeting, made a statement that 'We believe that the President of the United States is engaged in a cover-up'".
-Rep. Alexandria Ocasio-Cortez " Stonewalling Congress on witnesses and the unredacted Mueller report only enhances the president's appearance of guilt, and as a result, he has pushed Congress to a point where we must start an impeachment inquiry", Pocan said.
Republican Trump, who is seeking re-election next year, has aggressively sought to defy congressional oversight of his administration since Democrats took control of the House in January. In a letter to the House of Representatives Judiciary Committee, White House Counsel Pat Cipollone said Mr McGahn should not appear due to both "constitutional immunity" and "in order to protect the prerogatives of the Office of the Presidency".
The Committee wants her to testify on June 19th.
Trump then canceled an infrastructure meeting with top Democrats. "I don't think they should go on interminably".
Still, Democrats are continuing to escalate their requests for information.
Attorney General William Barr, the top USA law enforcement official and a Trump appointee, on May 2 snubbed the same committee, which later voted to hold him in contempt of Congress for not handing over a full, unredacted Mueller report.
During the closed-door meeting, Pelosi reportedly clashed with rank-and-file members who are upping the pressure on her to begin impeachment proceedings against the president.
Despite McGahn's absence, the committee held a hearing lasting about a half-hour that featured an empty chair at the witness table.
Their probes range from whether Trump obstructed justice during Special Counsel Robert Mueller's inquiry into Russian meddling in Trump's favor in the 2016 US presidential election to his personal finances and businesses.
An April CNN poll found that 69% of Democratic voters want Congress to take that step (though only 37% of Americans overall agree).
In his ruling from the bench, Ramos said he would not halt enforcement of the subpoena. "There were investigations going on three weeks ago when we met".
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