US President Donald Trump leaves the White House in Washington D.C. December 18, 2019. The US House of Representatives passed the impeachment against Donald Trump on Wednesday. Photo: Xinhua

US President Donald Trump pressed his Republican allies Thursday to exert rigid control of his Senate trial and ensure a swift exoneration, a day after he was impeached in a historic rebuke by the House of Representatives.

A bitter fight looms over the coming trial, expected to begin as early as the second week of January, with Senate leaders already drawing battle lines over the evidence that will be allowed.

But its fate was left in limbo late Thursday when the Senate's powerful majority leader, Mitch McConnell signaled the standoff with Democrats over trial particulars would continue into the new year.

"We remain at an impasse on these logistics," McConnell said on the floor, as he announced the Senate had completed its business until January.

Trump seized on the uncertainty to attack House Democrats for seeking to demand key witnesses or dictate how McConnell should run the process.

"I want an immediate trial!" he boomed on Twitter.

Trump is charged with abuse of office and obstruction of Congress but Democrats, who led the three-month House investigation, are threatening to delay sending the articles of impeachment to the Senate until they are reassured the process will be fair.

"I got Impeached last night without one Republican vote being cast with the Do Nothing Dems on their continuation of the greatest Witch Hunt in American history," Trump tweeted.

Trump is the third president in US history to be impeached. 

He suggested that the Democrats would "lose by default" if they decided not to show up at a date determined by the Senate.

The House voted along party lines Wednesday to charge Trump with abuse of power for pressuring Ukraine's president to investigate his potential White House challenger in 2020, the veteran Democrat Joe Biden.