DUP MP Ian Paisley has said his party is "holding out" until the Northern Ireland Protocol Bill advances further through Westminster before returning to Stormont power-sharing.
He was responding to reports that Downing Street fears the legislation to override the Brexit deal on Irish Sea trade could be defeated if the DUP does not commit to restoring the Assembly.
Patience with the party is "running thin" and "written assurances" are being sought that the DUP will nominate a Speaker, a UK government senior source told the News Letter.
Read more: Key points in Northern Ireland Protocol legislation and what happens next in Brexit dispute
The Times also reported that ministers will delay the next stage of the bill until the DUP formally commits to return to Stormont.
A second reading for the legislation has not been scheduled for next week or the week after, it was reported.
Mr Paisley said the DUP would show "good faith" if the bill goes through the houses "expeditiously".
"I spoke yesterday to the Secretary of State, and I spoke yesterday to other very senior members of the government," the North Antrim MP told the BBC's Good Morning Ulster programme.
"I think it's fair to reflect that their position is they want the re-establishment of the Northern Ireland Executive as quickly as possible.
"We want local government established, but we can only do it whenever we resolve these issues around the protocol, and we are holding out until we get those issues resolved.
"There will be a debate in parliament this month, a second reading of the Northern Ireland Protocol Bill. If that goes through parliament expeditiously I think that would be very helpful.
"And I think it would be then up to the House of Lords to make sure that they get it back to the House of Commons as quickly as possible thereafter.
"I think that under good faith we could show that we are a willing partner to make sure there is a government in Northern Ireland.
"It's in our interests and it's in the interests of the people of Northern Ireland, but it's also more importantly in the interests of the people of Northern Ireland that we have our place within the Union secured, and we can only do that if we get rid of the protocol."
On Wednesday the European Union launched fresh legal action against the UK in retaliation over the bill to unilaterally scrap parts of the protocol.
European Commission vice-president Maros Sefcovic accused the British government of setting out to "unilaterally break international law".
But the UK government has defended its actions, saying that measures are needed to ease the flow of goods from Great Britain to Northern Ireland and its "preference remains for a negotiated solution".
Read more: Key points in Northern Ireland Protocol legislation and what happens next in Brexit dispute
Read more: EU phone charger rules will become default across UK despite Brexit, says SDLP's Claire Hanna
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