David Cameron told MPs Mr Adams had accepted a role as “Baron of the Manor of Northstead”.
The Prime Minister’s statement that Gerry Adams had accepted a Crown title has been disputed by the Sinn Fein President.
David Cameron told the House of Commons Mr Adams had accepted the title in order to resign his Westminster seat.
In response, Mr Adams said he had not applied and had received an apology from the PM’s office.
Meanwhile, a treasury spokesman said that the Chancellor had appointed Gerry Adams to the title.
Parliamentary rules mean MPs cannot officially resign and have to accept a crown office to give up their seat.
A Treasury spokesman said on Wednesday: “Gerry Adams has said publicly that he is resigning from Parliament.
“Consistent with long-standing precedent, the Chancellor has taken this as a request to be appointed the Steward and Bailiff of the Manor of Northstead and granted the office.”
Earlier, David Cameron told MPs Mr Adams had accepted the role.
Speaking in response to a question from DUP MP Nigel Dodds, the Prime Minister said he was glad that the rules had been followed.
To laughter from MPs, he added: “I’m not sure that Gerry Adams will be delighted to be Baron of the Manor of Northstead. But nonetheless I’m pleased that tradition has been maintained.”
Later on Wednesday, Mr Adams said that when he was told of Mr Cameron’s remarks it was the first he had “heard of this development”.
In a statement he said the claim that he had accepted a crown title was “untrue” and that he had “simply resigned”
“I am an Irish republican,” he said.
“I have had no truck whatsoever with these antiquated and quite bizarre aspects of the British parliamentary system.”
He described Mr Cameron’s announcement as “bizarre” .
“I am sure the burghers of that Manor are as bemused as me,” he added.
“I have spoken to the Prime Minister’s private secretary today and he has apologised for today’s events.
“The onus is on the Westminster parties to call a by-election as soon as possible in the West Belfast constituency.”
On Tuesday, the Speaker’s Office told the BBC that it was its understanding that Mr Adams had not applied for the crown position and therefore remained an MP.
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