"We have to be careful to use the resources and the abilities of the House majority in a focused and a responsible way," Coons said on CNN . "We need to focus on things that are relevant and matter to the average American."

Mueller submitted his report to the Justice Department on Friday, nearly two years after he was tapped to lead an independent probe into Moscow's efforts to influence the 2016 elections and whether the Trump campaign colluded with Russia.

Attorney General William Barr, in a letter to Congress on Friday evening, said he "may be in a position" to brief lawmakers on Mueller's "principal conclusions" as early as this weekend.

"I remain committed to as much transparency as possible, and I will keep you informed as to the status of my review," he wrote.

The news that Mueller had submitted the long-anticipated report rippled quickly across Capitol Hill and beyond, with members from both parties issuing a blizzard of statements calling for the full report to be made public.

Barr has not committed to doing so, saying during his confirmation hearing before the Senate in January that he would disclose "as much information available as I can consistent with the rules and regulations that are part of the special counsel regulations." He left open the possibility that he may keep parts of the report undisclosed under claims of executive privilege.

The contents of the report remain unknown, although Mueller is not recommending any more indictments as part of his investigation, a Justice Department official said late Friday.

Republicans are viewing that news as vindication that Trump had committed no wrongdoing related to Russia's efforts to interfere in the election to help him win.

Apart from the Mueller probe, Democrats have launched a series of wide-ranging investigations of their own into Trump's actions, including his relationships with Russian officials and business figures.

"The American people have a right to the truth," they said.