Congressman Jason Crow, a Democrat from Colorado, speaking on behalf of the House managers, called impeachment an "extraordinary remedy" and "a tool only to be used in rare instances of grave conduct."
White House counsel Pat Cipollone defended the president by accusing Democrats of an attempt to "overturn the results of one election and to try to interfere" in the ongoing presidential race.
The two sides have up to four hours, equally divided for them, to make their own case.
After the closing arguments wrap up, the Senate is expected to reconvene in legislative session, in which senators are allowed to speak on the impeachment case.
Senators will vote on articles of impeachment against Trump on Wednesday, according to a resolution it adopted last week.
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 November 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 can only happen in the Senate and requires at least two-thirds of its members, or 67 senators, to vote in favour 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 )