If the House impeaches, the Republican-held Senate would then hold a trial on whether to convict Trump and remove him from office. Despite the current lack of support for the inquiry among Senate Republicans, McConnell said the chamber by rule would have no choice but to follow through with the process.

House Speaker Nancy Pelosi on Tuesday announced the start of an impeachment inquiry into Trump amid scrutiny over whether he tried to influence the 2020 election by urging Ukraine's president to investigate the family of Joe Biden, the former vice president and one of his chief rivals for the presidency. The House Intelligence Committee's investigation could lead to a full chamber vote to impeach the president.

"I would have no choice but to take it up," the Kentucky Republican told CNBC. "How long you are on it is a different matter, but I would have no choice but to take it up based on a Senate rule on impeachment."

The Senate would have to take up impeachment of President Donald Trump if the House effectively votes to charge the president, Senate Majority Leader Mitch McConnell said Monday.

The Senate as currently composed is unlikely to remove the president from the White House. It would need a two-thirds majority vote to do so.

Last week, House Democratic support for starting an impeachment inquiry swelled as more information surfaced about the president's interactions with Ukrainian President Volodymyr Zelensky. A whistleblower complaint made public last week raises concerns that Trump abused his power to influence the 2020 election and that the White House tried to cover up a call between Trump and Zelensky.

At least 226 House members — all Democrats except for one independent — now favor some kind of action on impeachment, according to an NBC News tally. The chamber would need 218 votes for a simple majority to impeach Trump.

McConnell on Monday argued the Democratic-held House has not focused enough on passing legislation it knows the Senate would approve. He contended the party has a "thin record" of passing bills that could actually become law

"If I were the speaker, I wouldn't want to go into next year's election having it credibly said that all you did for the whole Congress was harass the president and try to remove him from office," he said.

In a statement responding to McConnell, Pelosi spokesman Drew Hammill pointed to the fact that the top Senate Republican has called himself the "Grim Reaper" of House-passed legislation such as bills designed to expand gun background checks and curb government corruption. McConnell on Monday called them "left-wing proposals."

Hammill said Democrats "have passed scores of significant legislation now sitting on Senator McConnell's desk."

"House Democrats will continue to make our agenda too hot for Senate Republicans to handle, and there will be a price to pay for obstructing the People's business," he said.

As the impeachment inquiry intensifies, Trump has increasingly lashed out over what he calls a "witch hunt" intended to distract from his successes. Earlier Monday, he suggested House Intelligence Committee Chairman Rep. Adam Schiff, the Democrat leading the impeachment investigation, could face "arrest for treason." Only hours before, he shared a quote from a Fox News guest that suggested Trump's impeachment could lead to civil war.

Asked about Trump's rhetoric on Monday, McConnell did not directly address it.

"What I want to do is spend our time accomplishing things for the American people," he said.