A day after several dozen GOP lawmakers in the House invaded a secure hearing room at the U.S. Capitol and disrupted the impeachment testimony of a Pentagon official, Republican Senators unveiled a resolution demanding that House Democrats vote first to officially authorize any such investigation.

"I consider it to be out of bounds with what we have done in the past," said Sen. Lindsey Graham (R-SC), who has been one of the main defenders of President Donald Trump.

"It's unfair to the President and dangerous to the Presidency," Graham told reporters at a Senate news conference.

“There's a right way to do it and a wrong way to do it,” Graham added, as he was part of the impeachment effort twenty years ago involving President Bill Clinton.

"It is a hyper-partisan process completely void of due process," said Sen. Kevin Cramer (R-ND). "It is a disservice to the American people."

House Democrats have said there is no rule which forces them to take a vote to authorize an impeachment investigation - even as they acknowledge that was done in the past for Presidents Nixon and Clinton.

While GOP lawmakers disrupted a deposition on Wednesday, the three committees involved in this process are expected to work this weekend, with testimony from a former staffer on the White House's National Security Council.

Democrats say Republicans are just trying to do everything they can to steer the debate away from the details of the Ukraine investigation, and the possible impeachment process.

It wasn't immediately clear if GOP leaders would try to force a vote on the resolution in the Senate.

Graham said some Republicans have urged him to force Rep. Adam Schiff (D-CA) to testify - as Schiff has led the impeachment effort for House Democrats.

But Graham told reporters that would probably not work.