Senate Democratic leader Chuck Schumer said Mr Trump “just walked out” of a meeting with him and House Speaker Nancy Pelosi in a “temper tantrum”.
Mr Schumer said Mr Trump asked Ms Pelosi at Wednesday’s White House meeting whether she would agree to fund his wall on the southern border with Mexico.
When she said “no”, Mr Schumer said, the President got up and said: “Then we have nothing to discuss”, adding: “And he just walked out”.
In a tweet, Mr Trump branded the meeting “a total waste of time” and said he had said: “bye-bye, nothing else works”.
He said: “Just left a meeting with Chuck and Nancy, a total waste of time.”
He went on: “I asked what is going to happen in 30 days if I quickly open things up, are you going to approve Border Security which includes a Wall or Steel Barrier?
“Nancy said, NO. I said bye-bye, nothing else works!”
Vice President Mike Pence denied suggestions that Mr Trump had had a “temper tantrum”, saying: “I don’t recall him ever raising his voice”.
He said Democrats were “unwilling to even negotiate” an end to the partial government shutdown.
“I think the president made his position very clear today that there will be no deal without a wall,” he said after the meeting.
He said Mr Trump asked Ms Pelosi whether she would be willing to agree to funding for a wall or a barrier on the southern border if he re-opened the government quickly.
Mr Pence said: “When she said ‘no’, the president said ‘goodbye’.”