Senior nationalist figure Mark Durkan hit out at the Sinn Fein president’s comments, which he made on Saturday in Dublin at Sinn Fein’s annual conference.
Mr Durkan was joined in his criticism by Dr Alasdair McDonnell, another former SDLP leader, who said Mr Adams had been “a slow learner” when it came to the principle of non-violence, unlike Mr Hume.
Mr Adams had told the conference “one of our great achievements has been, with John Hume and others, to build a peace process”.
He then repeated the point in an RTE interview, saying “one of the great achievements in Irish history – John Hume was there, others were there, but I and Martin McGuinness were there – was to bring about a peace process”.
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Mark Durkan, ex-SDLP MP for Foyle, who led the party from 2001 until 2010, was one of John Hume’s key negotiators in the run-up to the Good Friday Agreement.
He said Mr Adams appeared to be trying “to wrap the peace process around himself and around Sinn Fein”.
He said: “The fact is Sinn Fein resisted the arguments for peaceful methods, and through the peace process basically adjusted their position.
“Adams now tries to make it sound as though the peace was created by them, as though they had nothing to do with creating any of the violence.
“The role of John Hume is very different from the role of Gerry Adams...
“John Hume has always argued there was a democratic and peaceful path available.
“The democratic, peaceful alternative was always there, contrary to what Sinn Fein would pretend, where they portray the violence of the PIRA as though it was a necessary or inevitable prelude to what became the peace process.”
Whilst he suggested that Mr Adams was trying to “put himself on a par” with Mr Hume, and that Sinn Fein presents itself as “the authors of peace”, republicans had been slow to accept key peace milestones like the Mitchell Principles and the authority of the reformed police force.
And whilst Sinn Fein speak of a “rights-based approach” to issues nowadays, “all during the IRA campaign there was strong rights-based argument for a purely peaceful approach that Sinn Fein for long rejected”.
“It’s a slanted, inverted view of history,” said Mr Durkan.
However, he also criticised historical “revisionism” in the DUP, saying its leaders today behave “as though they are the arbiters of what the Good Friday Agreement means”, when they had bitterly opposed it at the time.
Mr McDonnell, ex-SDLP MP for South Belfast, who led the party from 2011 to 2015, said: “All I’d say is Gerry was a very late convert to peace. And he’s probably still on the road to Damascus. He’s not quite there.
“It required considerable persuasion by John Hume and by the Irish government and by various others to basically bring him into a political process, into a peace process.
“He was a slow learner – he came late to the peace idea.”
Writing in The Guardian on Monday (about a new film called ‘In the Name of Peace: John Hume in America’), fellow SDLP veteran Seamus Mallon said Sinn Fein was “wet-nursed” into the political process by men like Mr Hume, only to lead to the “bitter irony” of today’s “self-indulgent stand-off” with the DUP.
Mr Adams has repeatedly and consistently denied being a member of the IRA, and has denied that Sinn Fein and the IRA are the same organisation.
However, in 2015 he said he would never “disassociate” himself from the paramilitary group, and an official assessment of the terror group that year found that “PIRA members have been directed to actively support Sinn Fein,” and they “believe that the Provisional Army Council oversees both PIRA and Sinn Fein”.
In his speech to this year’s ard fheis – during which he announced that his 35-year-long presidency of the party will end in 2018 – Mr Adams said he has been “enormously privileged to be part of an amazing and evolving collective leadership”.
He said this leadership has included IRA border campaign veteran John Joe McGirl, IRA leader Joe Cahill, IRA commander-turned-politician Martin McGuinness, IRA arms smuggler-turned-TD Martin Ferris, among other members of Sinn Fein.