“He's a low life,” Mr. Trump added.
At one point, the President cited Schiff's criticism of Secretary of State Mike Pompeo.
"That guy (Schiff) couldn't carry his (Pompeo) blank strap, you understand that?" the President added, referring to a jock strap.
Later, at a joint news conference with the leader of Finland, the President was asked several times why he wanted the government of Ukraine to look at the Bidens.
“Biden and his son are stone cold crooked,” Mr. Trump said, as he refused to answer the questions posed by reporter Jeff Mason of Reuters.
Mr. Trump also again raised doubts about the story of the whistleblower inside the U.S. Intelligence Community, who raised questions about what the President said to the leader of Ukraine in a late July phone call.
"This country has to find out who that person was, because that person is a spy," Mr. Trump said of the whistleblower, as he denounced the whistleblower report as 'vicious.'
"The whistleblower was so dishonest," the President added, charging the person had badly misrepresented the call between Mr. Trump and the leader of Ukraine.
The President's comments came soon after top Democrats made clear they were pushing ahead swiftly on their impeachment investigation.
"We are concerned that the White House will continue to stonewall," Schiff said, as Democrats charge the White House has done everything possible to avoid having testimony from anyone in the Trump Administration.
“He is stooping to a level that is beneath the dignity of the Constitution,” House Speaker Nancy Pelosi said of the President.