With Lamar Alexander making the announcement on Thursday night, it was clear that the Democrats will not have the majority to force the Senate to call witnesses.
The course of the trial hinged on four Republicans who were waverning.
Of them, Susan Collins declared that she would vote with Democrats on the witness issue, while the two others, Mitt Romney and Lisa Murkowski, said they would announce their decision on Friday.
If the two still undecided Aenators go with the Democrats, there will be a tie in the 100-member Senate which has 53 Republicans, which means the motions to call witnesses will fail.
US Supreme Court Chief Justice John Roberts, who is presiding over the trial, can cast a tie-breaker vote, although it is considered unlikely that he will step into the polarised political maelstrom, preferring to stay neutral.
Alexander and Collins announced their decisions after the Senate finished its two days of questioning the prosecutors from the Democrat-controlled House of Represenatives which impeached Trump, and the President's legal team.
The next stage in the Senate trial is to vote whether to convict or acquit Trump, but Democrats want to prolong the trial with more witnesses.
Trump's acquittal, which requires a two-thirds majority is a foregone conclusion, and the Democrats strategy has been to use the impeachment to embarrass Trump as a campaign strategy for the November election.
Trump is charged with abuse of power because he requested Ukraine President Volodymyr Zelensky to probe the dealings of former Vice President Joe Biden and his son, Hunter, in that country.
He is also charged in the House impeachment with obstruction of Congress for refusing to allow some witnesses to testify before House investigators and produce documents they requested.
Democrats want to call John Bolton, who was fired as National Security Adviser by Trump, to testify.
He is reported to have written in the manuscript of a book that Trump froze $371 million in military aid to Ukraine to pressure Zelensky to probe the Bidens.
Joe Biden is the leading contender for the Democratic Party nomination to challenge Trump's re-election bid and asking Ukraine to investigate him amounts to abuse of power and inviting foreign interference in US election, Democrats maintain.
(Arul Louis can be contacted at arul.l@.in and followed on Twitter @arulouis)
( With inputs from IANS )