Trump told reporters in New York that he did not pressure Ukrainian President Volodymyr Zelenskiy in a July phone call to launch a corruption investigation into Biden and his son in return for U.S. military aid.
"No I didn't," Trump said.
A U.S. whistleblower lodged a complaint about the contents of Trump's conversation with Zelenskiy, leading to calls from some Democrats that Trump be impeached for trying to enlist a foreign power to smear a domestic opponent.
Biden, a former vice president, whose son Hunter worked for a company drilling for gas in Ukraine, is the front-runner in the race for the Democratic nomination to face Trump in the November 2020 election.
Trump gave a contradictory message about whether he would release a transcript of the call with the Ukrainian leader.
"I may do it because it was a very interesting call," Trump said. "It was a very nice call. I hope you get to see it and I hope you get to see it soon,” he said.
But he added: "I don't think it's a great precedent to be releasing calls with foreign countries, heads of foreign countries. So I don't think it's a great precedent."
Earlier on Monday, Trump shrugged off the impeachment talk, saying he was not taking it seriously.
DEMOCRATS SEEK DOCUMENTS
Democratic leaders of the House of Representatives have called a caucus meeting for Tuesday afternoon to discuss the whistleblower complaint, a leadership aide said.
Congressional Democrats on Monday demanded documents from the White House about the Trump team's contacts with Ukraine.
Three House committees - Intelligence, Foreign Affairs and Oversight - called on Secretary of State Mike Pompeo to produce documents related to contacts between Trump's lawyer Rudy Giuliani and Ukrainian officials.
The Democratic-led committees said in a letter that they "jointly request documents related to reported efforts by President Trump and his associates to improperly pressure the Ukrainian government to assist the president's bid for reelection."
Seven first-term Democratic lawmakers also inched closer to calling for Trump's impeachment, writing in an op-ed in the Washington Post: "If these allegations are true, we believe these actions represent an impeachable offense."
Trump hit out on Monday at Biden, calling him and his son "corrupt."
Neither the president nor aides have provided any details of possible corruption by Biden when he was vice president under Trump's predecessor, Democratic President Barack Obama.
There has been no evidence so far that Biden used his position as vice president to help his son, and he said in Iowa this past weekend that he had never discussed Hunter Biden’s business in Ukraine with his son.
Ukrainian officials, while acknowledging they had met with Giuliani, have not said that they would open any investigation of Biden or his son.
Ukraine's former general prosecutor, Yuriy Lutsenko, told Reuters on Friday that there was no evidence of wrongdoing on the part of Biden's son in his relationship with the energy firm.
JULY 25 CALL
The Wall Street Journal and the New York Times reported on Friday that Trump repeatedly asked the Ukrainian leader in the phone call to investigate the involvement of Biden's son with the company. He also asked Zelenskiy to work with Giuliani, who had been urging Ukrainian officials to investigate the Bidens.
On Sunday, Trump acknowledged that he discussed Biden and his son in the July 25 call.
Republican Senate Majority Leader Mitch McConnell said the Senate Intelligence Committee was working to get the intelligence community's inspector general to speak to the panel to discuss the whistleblower's allegations.
A Senate aide said a briefing with the panel's chairman and vice chairman was expected to occur this week.
The media reports about the phone call said Trump repeatedly asked Zelenskiy to investigate whether Biden misused his position as vice president to threaten to withhold U.S. aid unless a prosecutor who was looking into the gas company in which Biden's son was involved was fired.
Biden has confirmed he wanted the prosecutor fired but denies it was to help his son. Biden said the wider U.S. government, the European Union and other international institutions also wanted the prosecutor fired for his alleged failure to pursue major corruption cases.
A top official in Zelenskiy's administration told Reuters that Ukraine wanted to stay out of the domestic political battle in Washington and that any attempt by either side to take advantage of Ukraine would damage relations.