In a strict 53-47 party-line vote in the early hours of Wednesday, local time, the senators backed the trial plan offered earlier by Republican majority leader Mitch McConnell.
It allows the House 'managers', who are acting as prosecutors, to present their opening arguments later on Wednesday and delays a debate over whether to call witnesses until the middle of the trial.
The Republicans agreed to soften their previous plans to cram the 24 hours of opening arguments for each side in just two days. Instead, those 24 hours will be spread over three days. However, the resolution means that the trial will be held largely on the Republicans' terms.
The voted to block the Democrats' demand comes as a move was initiated by Senate Democratic Leader Chuck Schumer, saying earlier that the Democratic party will offer a number of amendments in relation to documents and witnesses relevant to the impeachment trial.
Later on Tuesday, Senate Republican leader McConnell also moved to block the Democrats' demand to subpoena the US State Department for certain documents and records related to the impeachment case. The Senate Republicans voted to block the demand in a 53-47 party-line vote.
After the three Democratic amendments were rejected, Schumer offered a fourth one to subpoena acting White House Chief of Staff Mick Mulvaney. The Senate voted the move down.
In his fifth attempt, Schumer offered an amendment to subpoena "all documents, communications, and other records within the possession, custody, or control of the Department of Defense" involving aid to Ukraine. The effort was voted down by the Senate.
On Monday, McConnell drafted a resolution giving House Democrat prosecutors and Trump's defense 24 hours over two days to present their respective cases before allowing senators to vote on whether to call witnesses or hear new evidence.
On 19 December, the House of Representatives voted to impeach Trump for abuse of power and obstruction of Congress. President Trump has continuously slammed the accusations against him as an "impeachment hoax" aiming to reverse the outcome of the 2016 election.
MNA/SPUTNIK