As the White House mounted a furious assault on the Mueller report and critics of a president not found to have conspired with Russia but not cleared of obstruction of justice, the chair of the House judiciary committee said obstruction, if proven, “would be [an] impeachable” offence.

Trump’s personal lawyer Rudy Giuliani toured the Sunday talk shows, arguing with interviewers in a series of chaotic encounters.

On Fox News Sunday, he claimed Robert Mueller’s 448-page report, which was released with redactions on Thursday, was full of “calumny, lies and distortion”.

On CNN’s State of the Union, the former New York mayor called one of Mueller’s lawyers a “hitman” and claimed the special counsel’s team “came close to torturing people” in questioning and confining Trump campaign chair Paul Manafort, who was convicted and sentenced on financial charges.

Asked on NBC’s Meet the Press why Trump was so angry at Mueller and former White House counsel Don McGahn, a key witness, Giuliani replied: “Because they tried to frame him.”

There’s nothing wrong with taking information from Russians. It depends on where it came from Rudy Giuliani

The first volume of Mueller’s report concerns Russian election interference and the Trump campaign’s warm reception to “offers of assistance” including an infamous June 2016 meeting with a Kremlin-linked lawyer offering “dirt” on Hillary Clinton.

Giuliani told CNN: “There’s nothing wrong with taking information from Russians. It depends on where it came from.”

On ABC’s This Week, White House adviser Kellyanne Conway, who previously called the inquiry a “a political proctology exam”, took a different tone, saying: “The campaign I managed in those last few months did not welcome help from Russia. In fact, I don’t recall getting, being offered help from Russia. It would have been a ridiculous prospect.”

In his second volume, Mueller considers potential obstruction of justice by Trump or his campaign, of which 11 instances are listed. He passed judgment on the issue to Congress.

House judiciary committee chair Jerrold Nadler told NBC that if evidence shows Trump obstructed justice, “some of this would be impeachable, yes”. He added that Democrats plan to “go where the evidence leads”.

Democrats remain split on impeachment, which would begin in the House they control but almost certainly fail in the Republican Senate. Some fear it would galvanise Trump’s supporters and win him sympathy among independents.

On Fox, House intelligence chair Adam Schiff said to impeach or not to impeach was “going to be a very consequential decision and one I’m going to reserve judgment on until we have a chance to fully deliberate on it”.

Oversight chair Elijah Cummings told CBS’s Face the Nation he could “foresee [impeachment] possibly coming”. But he said: “We have to be very careful here. The American people, a lot of them clearly still don’t believe that President Trump is doing things to destroy our democracy and has done a lot of things very poorly.”

He also said he thought “history would smile upon us for standing up for the constitution”.

The American people, a lot of them clearly still don’t believe President Trump is doing things to destroy our democracy Elijah Cummings

Giuliani fiercely attacked McGahn, who is cited by Mueller in descriptions of orders from Trump to fire the special counsel, which McGahn did not do.

McGahn’s recollections were “wrong”, Giuliani said on CNN, claiming the experienced lawyer was “confused [and] cannot be relied upon”. Mueller depicts McGahn taking notes of meetings with Trump, a practice Trump is said to have questioned. The Trump campaign has severed links with the law firm to which McGahn returned.

An incensed Giuliani made the “hitman” claim about Andrew Weissmann, a prosecutor Trump allies claim is too close to the Clintons.

“I have no problem with investigating Russian interference in the election,” Giuliani said, adding: “The reality is, you think this is the first time the Russians have interfered with a presidential election?”

Special counsel Robert Mueller and his wife Ann Cabell Standish leave St John’s Episcopal Church in Washington. Photograph: Andrew Harnik/AP

Giuliani was pressed on criticism of Trump by the 2012 Republican nominee, Mitt Romney, who said he was “sickened at the extent and pervasiveness of dishonesty and misdirection by individuals in the highest office of the land, including the president”.

“Stop the bull, stop this pious act,” Giuliani said, adding: “Who says [taking information from Russians is] even illegal? … And then does the information turn out to be false, by the way?”

Referring to Democratic party emails hacked by Russia and obtained by WikiLeaks, he said: “The information that was gleaned and disseminated, every newspaper printed it. Why did the Washington Post print the information that came from a foreign source, when they knew it was hacked? Aren’t they just as wrong for doing that as the campaign wanting to use it?”

Of Giuliani’s claim there was “nothing wrong with taking information from Russians”, former US attorney Preet Bharara, who was fired by Trump in 2017, told CNN: “That’s an extraordinary statement and I would hope he would retract it.”

Giuliani ran against Romney for the 2008 Republican nomination, both losing to John McCain. Asked if he would have accepted such information, Giuliani said: “I probably wouldn’t. I wasn’t asked. I would have advised, just out of excess of caution, don’t do it.” He also accused Romney of doing “things very similar”, although he did not elaborate.

Asked if Trump thought Russian interference helped him win, Giuliani told NBC: “Whether he did or he didn’t, I think it’s quite clear that there are a lot of factors that go into any election and the reality is he was elected president.”

Conway told ABC Trump “didn’t need WikiLeaks. We had Wisconsin. He won because he was the better candidate”.

Trump has repeatedly claimed Mueller’s investigation exonerated him, which it did not, and called the inquiry a “hoax”. He continued to tweet on Sunday, from his club in Florida.

Attending church, the president was asked if he felt betrayed by staffers who spoke to Mueller. According to the White House pool report, he “clearly heard the question” but “just smiled and turned away”.