The DUP has said Ian Paisley was not speaking on behalf of the party after the MP argued the Windsor Framework does not meet their seven tests.
It comes after a report from a unionist think tank which Mr Paisley chairs rejected the UK and European Union's new deal on Brexit's Northern Ireland Protocol.
The Centre for the Union paper, co-authored by loyalist activist Jamie Bryson, said the agreement offers "no sound basis" for the DUP ending its Stormont boycott over the Irish Sea trading arrangements.
Read more: NI Protocol deal analysis: Focus shifts to DUP as Windsor Framework is agreed
But the report said the Windsor deal is a "significant step forward" which could "with some necessary improvements" resolve unionist concerns.
In a foreword for the paper, Mr Paisley said his "instinctive reaction" to the Windsor Framework is that "the problem is not yet solved".
He added: "The report concludes that further concessions or 'components' must be 'bolted onto' the framework and it will be for unionists to determine what those concessions should be but until then, the Windsor Framework cannot be supported by unionists as a solution to the protocol."
For the past year the DUP has been blocking Stormont power-sharing in protest against the protocol, which angered unionists for creating new barriers on trade from Great Britain to Northern Ireland.
The Windsor Framework includes a new red and green-lane system for trade and an "emergency brake" for Stormont on future changes to EU goods rules applying to the region.
Speaking on BBC's Nolan Live, Mr Paisley said he does not believe the Windsor Framework meets the party's seven tests to end its veto on Stormont power-sharing.
The North Antrim MP said: "I don't believe it meets our tests and there's probably six or seven reasons why.
"For example, EU law will continue to apply in Northern Ireland. The brake only applies to future law, not to existing EU law; this is not of course a legal agreement, this is a political statement; physical checks will continue even in the green channel as it's called; the European Court of Justice will remain in the words of von der Leyen the 'final arbiter'; state aid issues are still not clear."
In a statement, a DUP spokesman said: "Ian Paisley, as he indicated, was speaking as chair of Centre for the Union rather than the DUP.
"The party is assessing the Windsor Framework against its seven tests and consulting following the publication of that framework.
"Upon completion of that process it will be for the party collectively to set out its position and next steps."
The Centre for the Union report includes a legal analysis from former Northern Ireland Attorney General John Larkin KC, who represented a unionist collective in an unsuccessful Supreme Court challenge to the protocol.
The barrister said the Windsor Framework does not strengthen the constitutional status of Northern Ireland as part of the UK.
Mr Larkin concluded: “Are the proposals contained within the Windsor Framework compatible with the Acts of Union 1800, particularly Article VI thereof? No.
"Do the proposals contained within the Windsor Framework remedy the 'subjugation' of Article VI of the Acts of Union 1800? No.
"Do the proposals in the Windsor Framework strengthen the constitutional guarantee respecting the constitutional status of Northern Ireland? No."
Meanwhile, former DUP deputy leader Lord Nigel Dodds has raised concerns about border control posts remaining at Northern Ireland's ports.
Speaking in the House of Lords, he said: "The provision of these border control posts actually disrupts the UK single market for goods and replaces it with a Great Britain single market for goods and an all-Ireland single market for goods."
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