Amid the squabble over the timing and scope of the release, a senior Republican senator assured that Attorney General Bill Barr will release the special counsel's findings in a matter of "weeks, not months."
The Republican-led upper chamber has faced mounting pressure to align with a measure from the Democrat-controlled House of Representatives that seeks swift release of the full report to Congress and the American people.
Senate Democrat Diane Feinstein took to the Senate floor asking for unanimous consent to pass the non-binding resolution, which cleared the House in mid-March by 420 to 0.
"The fact is that a four-page summary cannot possibly illuminate what this thorough of an investigation uncovered," said Feinstein, referring to Barr's summary description of the report.
Senate Majority Leader Mitch McConnell objected, stressing the need for Mueller and Barr to review the report and determine what can be publicly released and what must be redacted.
"I think we should be consistent in letting the special counsel actually finish his work and not just when we think it may be politically advantageous to one side of the other for him to do so," he said.
While Mueller found there was conclusive evidence that Russia influenced the vote, Barr in his summary cleared Trump and his team of any collusion with Russia regarding election interference.
Two previous efforts by Senate Minority Leader Chuck Schumer to advance the House measure were also blocked, actions the top Democrat denounced on the Senate floor Wednesday.
"When we read reports that Barr only wants to release a summary and Leader McConnell is unsupportive of transparency, something doesn't smell right," Schumer said.
Senate Judiciary Committee chairman Lindsey Graham meanwhile said he met with Barr Monday and the attorney general laid out a path for reviewing the report with Mueller and releasing it.
"He's going to do all that in weeks, not months; he's going to turn it over to the committee, then I think he'll come to the Senate, hopefully some time in April" to testify, Graham told Fox News.