The Judiciary Committee is expected to draft at least three articles of impeachment -- essentially charges of wrongdoing -- against Mr Trump which the whole House of Representatives is expected to vote on before Christmas.
Those articles could include abuse of power through bribery, obstruction of Congress and obstruction of justice.
If the House does vote to impeach the president as expected, the Senate will hold a trial next year. In theory it could remove him from office, or censure him, if two-thirds of senators vote to do so. But since the upper house is controlled by his Republican allies it looks unlikely to do so.
This weekend also saw the publication of a report by the Judiciary Committee setting out the constitutional basis for impeachment.
It refers to the writings of George Washington and Thomas Jefferson and follows a hearing last week in which three of four constitutional law experts giving evidence said they believed Mr Trump's actions had met the bar for impeachment.
The president is accused of abusing his power by pressuring his Ukrainian counterpart Volodymyr Zelensky to smear his Democratic opponents in return for releasing foreign aid and arranging a symbolically important White House meeting.
Mr Trump kept up his angry denials and counter-accusations on Twitter on Saturday, at one point claiming that he was the "greatest of all presidents".
"Not only have the Democrats not advanced key pieces of legislation that would help the economy, but the polls, especially in early states, are showing that voters are tuning out." @PeteHegseth They don't want our greatest of all presidents impeached!
— Donald J. Trump (@realDonaldTrump)
Quoting a Fox News host he wrote: "'Not only have the Democrats not advanced key pieces of legislation that would help the economy, but the polls, especially in early states, are showing that voters are tuning out.' @PeteHegseth They don't want our greatest of all presidents impeached!"
Jerrold Nadler, chairman of the Judiciary Committee, said the president's actions represented the "worst nightmare" of the Founding Fathers.
He said: "President Trump abused his power, betrayed our national security, and corrupted our elections, all for personal gain.
"The Constitution details only one remedy for this misconduct: impeachment.
"The safety and security of our nation, our democracy, and future generations hang in the balance if we do not address this misconduct. In America, no one is above the law, not even the president."
On Monday the Intelligence and Judiciary Committees will present their reports ahead of the articles of impeachment being decided on.
Only two US presidents have been impeached before – Andrew Johnson in 1868 and Bill Clinton in 1999 – but both were acquitted in their Senate trials. Richard Nixon resigned in 1974 while impeachment proceedings were being prepared against him.