The US attempt to extradite Julian Assange is the “the Dreyfus case of our age”, John McDonnell has said, as Europe’s human rights watchdog added her voice to opposition to the move.

The shadow chancellor paid a two-hour visit to see Assange in Belmarsh prison in London on Thursday and said Britain’s standing in the world would be severely damaged if the extradition went ahead

On Wednesday it was claimed in a London court that Donald Trump had offered Assange a pardon if he would say Russia was not involved in leaking Democratic party emails.

McDonnell likening the plight of Assange to Alfred Dreyfus, the 19th-century Jewish French army officer who was tried and convicted on charges of treason amid a climate of antisemitism.

“I think this is one of the most important and significant political trials of this generation,” the shadow chancellor said. “In fact, longer. I think it is the Dreyfus case of our age, the way in which a person is being persecuted for political reasons for simply exposing the truth of what went on in relation to recent wars.”

Separately, the Council of Europe commissioner for human rights. Dunja Mijatović, said Assange should not be extradited because of the potential impact on press freedom and concerns about “the real risk of torture or inhuman or degrading treatment”, in contravention of the European convention on human rights.

Allowing the extradition would have “a chilling effect on media freedom, and could ultimately hamper the press in performing its task as purveyor of information and public watchdog in democratic societies”, she said.

“The indictment raises important questions about the protection of those that publish classified information in the public interest, including those that expose human rights violations. The broad and vague nature of the allegations against Julian Assange, and of the offences listed in the indictment, are troubling, as many of them concern activities at the core of investigative journalism in Europe and beyond.”

The extraordinary claim about the supposed offer of a pardon from Trump was made at a hearing at Westminster magistrates court on Wednesday before the opening next week of Assange’s legal case to block attempts to extradite him. Assange faces charges in the US for publishing hacked documents.

A former Republican congressman named by the Assange legal team as a key witness denied the pardon claim.

Assange’s lawyers alleged that during a visit to London in August 2017, congressman Dana Rohrabacher told Assange that “on instructions from the president he was offering a pardon or some other way out if Mr Assange … said Russia had nothing to do with the DNC [Democratic National Committee] leaks.”

Rohrabacher denied the claim, saying he had made the proposal on his own initiative, and that the White House had not endorsed it.

McDonnell said he and Assange had discussed the issue of the reported pardon but had not gone into great detail.

“We are hoping that in court he is able to defeat the extradition bid. We don’t believe that extradition should be used for political purposes, and all the evidence – even the recent revelations with regard to Trump engagement – demonstrates that this is a political trial and we are hoping that the courts will see it that way,” he said.

“If this extradition takes place it will damage the democratic standing of our own country as well as America. We have a longstanding tradition in this country of standing up for whistleblowers, journalists … if this extradition takes place I think it will damage our reputation.”

The comparison between Assange and Dreyfus drew criticism, including from the Community Security Trust (CST), a charity working against antisemitism and racism in British society, which tweeted: “Disgraceful false equivalence to one of the key learning moments of modern Jewish history.”

A protest in support of Assange is due to take place on Saturday in Parliament Square and will be addressed by political figures and others such as the music producer Brian Eno. McDonnell said he and others were calling on people to demonstrate peacefully.

He alluded to attempts to build a cross-party alliance to fight any extradition, adding that there were Tory MPs who he believed could come onboard. He also believed there were “deep doubts” in government, based on comments by Boris Johnson to Jeremy Corbyn about the unbalanced nature of the extradition treaty between the US and the UK

“The problems we have now is that when the hearings start they will be subjudice and it will be difficult to raise it in the House of Commons, but we will be looking to see how we can raise it as often as we possibly can, of course within parliamentary rules, but also build cross-party support, and as you know people like [the Conservative MP] David Davis have raised their concerns, so this is across parties in the House of Commons,” McDonnell said.

“I am hoping that combination of cross-party support, what has happened in the media, the exposes that have taken place in recent weeks, will ensure that we have a climate of opinion in this country that prevents this extradition taking place.”