Washington (CNN) Congressional Democratic leaders -- outraged over the Trump administration's rollout of special counsel Robert Mueller's report -- are calling on Mueller to publicly testify before Congress, renewing demands for the entire report to be released and raising concern over the President's conduct detailed in the report.

In a move that sets up a clash between the Trump administration and Congress, House Judiciary Committee Chairman Jerry Nadler issued a subpoena on Friday for the full report , giving the Justice Department until May 1 to comply.

"My Committee needs and is entitled to the full version of the report and the underlying evidence consistent with past practice," Nadler said in a statement. "The redactions appear to be significant. We have so far seen none of the actual evidence that the Special Counsel developed to make this case. Even the redacted version of the report outlines serious instances of wrongdoing by President Trump and some of his closest associates. It now falls to Congress to determine the full scope of that alleged misconduct and to decide what steps we must take going forward."

When asked at a news conference Thursday if the Mueller report would provide a "road map" should Democrats open impeachment proceedings, Nadler said it was "too early" to discuss that, but then said the special counsel "probably" wrote the report with that "intent."

In a joint statement, House Speaker Nancy Pelosi and Senate Minority Leader Chuck Schumer similarly drew a distinction between the words of Attorney General William Barr and special counsel Robert Mueller on the question of whether the President obstructed justice.

"The differences are stark between what Attorney General Barr said on obstruction and what Special Counsel Mueller said on obstruction," the Democratic leaders said in their statement, adding, "As we continue to review the report, one thing is clear: Attorney General Barr presented a conclusion that the president did not obstruct justice while Mueller's report appears to undercut that finding."

Pelosi and Schumer broadly criticized Barr earlier in the day on Thursday, accusing him of creating "a crisis of confidence in his independence and impartiality" and saying public testimony from Mueller himself in both the House and the Senate is "the only way to begin restoring public trust."

The call was echoed by Nadler, who posted to Twitter a copy of a letter to Mueller requesting testimony in front of the committee "as soon as possible" and "no later than May 23, 2019."

House Intelligence Committee Chairman Adam Schiff also announced that his committee has invited Mueller "to testify on the counterintelligence investigation." A letter from Schiff to Mueller states that the committee will work "to secure a mutually agreeable date in May."

During his Thursday morning news conference, Barr said he has "no objection" to Mueller testifying when asked if he would allow Mueller to testify publicly to Congress in light of the calls from Democrats.

Barr has blocked from public view portions of the report, including grand jury material, sensitive intelligence material, details about ongoing investigations, and information that harms the "privacy and reputational interests of peripheral third parties."

Democrats have slammed what they say are orchestrated attempts by the Trump administration to control the narrative surrounding the report's release. Prior to the report's release, they had also threatened to subpoena the Justice Department to obtain the full report if necessary, which may lead to a contentious court battle.

The Mueller report is the result of a nearly two-year investigation into how Russia interfered in the 2016 presidential election to help the Trump campaign and whether the President then obstructed that probe. Mueller brought criminal charges against 25 Russians who interfered in the election and six Trump associates: senior campaign officials Paul Manafort and Rick Gates, national security adviser Michael Flynn, former fixer Michael Cohen, longtime ally Roger Stone and campaign adviser George Papadopoulos.

During his news conference, Barr said the President has been right all along on whether the Trump campaign coordinated with the Russian government in interfering with the 2016 presidential election. "As he said from the beginning, there was, in fact, no collusion," Barr said.

Republicans claim vindication for the President

Some Republican allies of the President in Congress immediately seized upon the attorney general's initial announcement to claim exoneration.

Rep. Jim Jordan, Republican of Ohio, tweeted , "No collusion! No obstruction!"

House Republican leader Kevin McCarthy issued a statement saying, "Nothing we saw today changes the underlying results of the 22-month long Mueller investigation that ultimately found no collusion," and adding, "it is time to move on."

House GOP Whip Steve Scalise called on Democrats to apologize for "making outlandish claims about the President" and said in a statement that "while Washington Democrats hoped for the special counsel to deliver a collusion conclusion, this report instead delivered a death blow to their baseless conspiracy theories."

Democrats zero in on obstruction question

But the fallout from the report is far from over.

Some Democrats quickly zeroed-in on the episodes that Mueller examined concerning the President related to potential obstruction of justice.

Barr said that he concluded that "the evidence developed by the special counsel is not sufficient to establish that the President committed an obstruction-of-justice offense." He said that Trump, amid "relentless speculation in the news media about the President's personal culpability," was "frustrated and angered" that the probe undercut his presidency but that the White House still "fully cooperated" with it.

But Democrats rejected the attorney general's analysis.

Rep. Jamie Raskin, Democrat of Maryland, called it "ridiculous."

"Congress will be eager to analyze the ten (10) separate episodes of obstruction that AG Barr was so eager to contradict. But the argument that Trump lacked the intent to obstruct because he was 'frustrated and angry' is ridiculous," Raskin tweeted.

Democrats are also taking issue with the fact that Barr said during his news conference that counsel for the President had the chance to review the redacted report before its public release.

"Earlier this week, the President's personal counsel requested and was given the opportunity to read a final version of the redacted report before it was publicly released," Barr said.

Following the news conference, Pelosi said on Twitter, "AG Barr has confirmed the staggering partisan effort by the Trump Admin to spin public's view of the #MuellerReport -- complete with acknowledgment that the Trump team received a sneak preview. It's more urgent than ever that Special Counsel Mueller testify before Congress."

Many Democrats believed that Barr would mishandle the special counsel's investigation before he was even confirmed, pointing out that he had previously written that Mueller's obstruction of justice inquiry was flawed.

Their doubts deepened when he became attorney general. In March, he released a memo announcing that he and deputy attorney general Rod Rosenstein determined that there was not sufficient evidence to establish that Trump committed an obstruction-of-justice offense, while also acknowledging that Mueller did not exonerate the president.

Barr then said in a congressional hearing that "spying did occur" against the 2016 Trump campaign, a claim that Trump's reelection team then used to inaccurately assert that the attorney general had said he believed the Obama administration had illegally surveilled the President.

This story has been updated with additional developments Friday.