DUP minister Edwin Poots has warned the impasse over Brexit's Northern Ireland Protocol could lead to the "funeral of the Good Friday Agreement".
And DUP MP Ian Paisley said changes to the government's Westminster bill aimed at overriding the Irish Sea trading arrangements would mean "devolution never returns to Northern Ireland".
The senior party figures launched a renewed attack on the protocol as talks are due to resume between the UK and European Union in the latest attempt to resolve the impasse.
Read more: NI secretary wants to 'deliver enough pressure' to restore Stormont and fix Brexit Protocol
The DUP has blocked the restoration of Stormont power-sharing in protest over the protocol, which has introduced new trade barriers between Great Britain and Northern Ireland.
Sir Jeffrey Donaldson's party has backed the government's Protocol Bill, which is progressing to the House of Lords, as a potential means of addressing unionist concerns.
But during the Conservative Party conference, former deputy prime minister Lord Heseltine said he believed the bill would be "massacred" in the Lords.
Mr Poots said any delay due to peers changing the legislation would be "unacceptable and untenable".
The Agriculture Minister told RTE's Morning Ireland programme that if the bill "proceeds quickly that would be fantastic".
He added: "However, it is going into the House of Lords stage and if the House of Lords decide to delay it, that could go on for another nine months and that's just an entirely unacceptable and untenable position for us.
"There won't be a Stormont government until this issue is resolved, that's the circumstances we find ourselves in.
"Therefore, whenever Ireland invites President Biden to come over for the 25th anniversary of the Belfast Agreement in Easter next year, unless something radical happens and the EU decide to become a bit more realistic, then he will be coming over to the funeral of the Good Friday Agreement, not to the celebration of its 25th anniversary.”
On Monday, Prime Minister Liz Truss said there was "no reason" why a Stormont Executive and Assembly should not be re-established now and she wants a protocol settlement that "works for everybody".
Speaking on the BBC's Nolan Show, Mr Paisley said for every day that people "cling" to the protocol, there "will be no Assembly".
"So the great prize in all of this is fix it, resolve these issues once and for all, get Northern Ireland out of this economic mess that the protocol has put it into and we will see the Assembly re-established."
He added: "If the House of Lords molest that bill and massacre it as one senior member of the House of Lords said this week, well all they are doing is preventing the Assembly ever coming back."
Sinn Féin Agriculture Minister John O'Dowd urged the government to move away from the Protocol Bill, describing it as "breaking international law".
He said: "We need a British government who is committed to enacting its international obligations, to enacting the Good Friday Agreement and ensuring they're not giving anywhere for the DUP to hide from their responsibilities in forming an Executive."
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