"There is no good reason, no good reason that the special counsel's report should not be made public. The American people are overwhelmingly for the report being made public. They have a right to see it. No one should stand in the way of that," Schumer said from the Senate floor.

Graham stressed that he supported Mueller's probe into Russian interference in the 2016 election, and predicted that it would wrap up shortly. But he added that he had been "trying to find balance" by also supporting an investigation into Clinton-related scandals.

"Was there two systems of justice in 2016? One for the Democratic candidate and one for the Republican candidate?" Graham asked.

Under Senate rules, any one senator can try to pass or set up a vote on a bill, resolution or nomination. But, in turn, any one senator can block their request.

Schumer fired back that Graham appeared to be using a "pretext" for trying to block the Mueller resolution.

"I have absolutely no idea why a member of this body would object to this basic level of transparency whatever their concern or other issues," he said.

The House-passed resolution argues there is “overwhelming public interest” in the government releasing the contents of the high-profile report. The resolution calls on the DOJ to fully release the report to Congress and to release it to the public “except to the extent the public disclosure of any portion thereof is expressly prohibited by law.”