US Senate Majority leader Mitch McConnell has told senators privately that he does not yet have the votes to block new witnesses in Donald Trump’s impeachment trial.

Mr McConnell convened a closed-door meeting of his party’s senators shortly after Mr Trump’s legal team made its closing arguments in the trial on Tuesday.

The third and final day of defence proceedings was punctuated by revelations from former national security adviser John Bolton.

A Republican familiar with the meeting was not authorised to describe it and requested anonymity.

Mr McConnell faced a handful of potential defections but several days remain before any potential witness vote would be taken.

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Senator McConnell speaks during the trial (Senate Television via AP)

A decision to call more witnesses would need 51 votes to pass.

With a 53-seat majority, Republicans can only afford to lose three Republicans to prevent more debate over witnesses.

Mr McConnell has been trying to prevent a prolonged trial.

Republicans were warned that subpoenaing testimony from Mr Bolton or other witnesses could run quickly into legal challenges that could drag out for weeks.

But Republican senator Mitt Romney has said he wants to hear what Mr Bolton has to say.

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Former national security adviser John Bolton wrote in a manuscript that President Trump wanted to withhold military aid from Ukraine until it committed to helping with investigations into Democratic rival Joe Biden (Luis M. Alvarez/AP)

Two other Republican senators, Susan Collins and Lisa Murkowski, also want to hear from more witnesses.

The White House has blocked its aides from appearing in the impeachment proceedings and would almost certainly claim some sort of executive privilege or national security objections over Mr Bolton testifying.

One closely-watched Republican, retiring senator Lamar Alexander, told reporters as he left the private meeting he would wait for the next few days of the trial and make his decision.

Some senators have discussed trying to reach a deal with Democrats in which each side would call a witness – for example, Mr Bolton and Hunter Biden, the son of former vice president Joe Biden, whose work in Ukraine has been referenced by Mr Trump’s team in the impeachment proceedings.

However such a deal has had few takers as most Republicans do not want to hear from Mr Bolton and few Democrats want to draw the Bidens into the impeachment proceedings.