Senators, who act as the jury for the trial and aren't allowed to speak during the proceeding, will reconvene later in a legislative session, in which they are expected to speak on the impeachment case, Xinhua news agency reported.
They will vote on articles of impeachment against Trump on Wednesday afternoon, according to a resolution adopted last week.
In his closing remarks, Congressman Hakeem Jeffries, one of the seven House managers, said that they have proven their case against Trump with "a mountain of evidence."
White House counsel Pat Cipollone, for his part, urged senators to reject the articles of impeachment.
Monday's session came days after the Senate, where Republicans have a narrow majority over Democrats, voted to reject the effort in seeking witnesses and documents for the proceeding, paving the way for a quick end.
The House, controlled by Democrats, impeached Trump in December last year for abuse of power and obstruction of Congress, charges that the White House has refuted.
A whistleblower raised concern in an anonymous complaint last summer about the White House's interactions with Ukraine, triggering a Democrat-led impeachment inquiry against Trump.
The US president was alleged to have pressed his Ukrainian counterpart, Volodymyr Zelensky, into launching investigations that could politically benefit him. Furthermore, the White House allegedly tried to cover it up.
In a tweet on Monday, Trump called the impeachment a partisan "hoax," while lashing out at Democrats.
"Nothing will ever satisfy the Do Nothing, Radical Left Dems!" Trump wrote.
According to the US Constitution, the House shall have the "sole Power of Impeachment," while the Senate shall have the "sole Power to try all Impeachments."
Conviction, which will lead to removal of a president, can only happen in the Senate and requires at least two-thirds of its members, or 67 senators, to vote in favor of at least one article of impeachment after a trial. Currently, the Senate has 53 Republicans, 45 Democrats, and two independents who caucus with Democrats.
No sitting US president has ever been removed from office by Congress through impeachment.
( With inputs from IANS )