WASHINGTON — Senate Majority Leader Mitch McConnell, R-Ky., acknowledged to Republican senators during a private meeting Tuesday that he did not currently have the votes to avoid calling witnesses in President Donald Trump's impeachment trial, a GOP aide familiar with his comments told NBC News.

Although the votes are not yet secured, Republicans appeared confident Tuesday evening that they would ultimately succeed in blocking witnesses. Senate Republican leadership exerted strong pressure on the party's members to vote against calling witnesses, two sources familiar with the matter said.

The sources said Republican Senate leaders "whipped the vote" — although there was no official vote count — against calling for witnesses at the private GOP Senate meeting Tuesday afternoon, which came after Trump's defense team wrapped up its arguments. Whipping is when leaders firmly tell members how the party expects them to vote.

Several Republican senators wouldn't divulge the substance of what they discussed, telling reporters to "check with the whip" about any directives from leadership.

Sen. Kevin Cramer, R-N.D., said that he was "whipped against voting to call witnesses" but that there was not an official whip count.

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Sens. John Hoeven, R-N.D., and John Boozman, R-Ark., said, however, that they did not feel pressured. Boozman said everyone at the hourlong meeting was "respectful."

The meeting of the Senate Republican Conference was held for the purpose of "starting to check the conference on witnesses," a GOP leadership said. At a Senate Republican lunch ahead of the meeting, executive privilege was also expected to be discussed.

Conversations about where Senate Republicans are on the question of witnesses have been ongoing. A debate and vote could come later this week.

Republicans have a 53-47 majority in the Senate, meaning Democrats would need four Republicans to join them in a vote for witness testimony.

Top Senate Democrats have said repeatedly that they want former national security adviser John Bolton; acting White House chief of staff Mick Mulvaney; Robert Blair, senior adviser to Mulvaney; and Michael Duffey, associate director for national security at the Office of Management and Budget, to testify.

Calls for Bolton, in particular, to testify have intensified in recent days after The New York Times reported — according to a manuscript of Bolton's book, which it obtained and has not seen by NBC News — that Trump told Bolton in August that nearly $400 million in aid to Ukraine would not be released until it provided all of the information it had in connection with investigations of Democrats the president was seeking.

A pair of moderate Republican senators — Mitt Romney of Utah and Susan Collins of Maine — said Monday that the report of major revelations in Bolton's soon-to-be-released book strengthened the case for calling witnesses.

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Romney, Collins, Lisa Murkowski of Alaska and Lamar Alexander of Tennessee are considered the Republicans most likely to vote for witnesses.

Murkowski said Monday: "I've said before I'm curious about what Ambassador Bolton might have to say. I'm still curious." Alexander said he won't decide until after both sides have answered questions from the Senate.

Sen. Lindsey Graham. R-S.C., a top Trump ally who's resisted calls for additional witnesses and documents, acknowledged Monday that Bolton may be "a relevant witness" and said he'd consider subpoenaing a manuscript of his book.