Former first minister Paul Givan was speaking after parties met the head of the NI Civil Service.
It would take a miracle for an executive at Stormont to be restored by next week’s deadline, a senior DUP politician has said.
Northern Ireland Secretary Chris Heaton-Harris has said he will call another election if power-sharing has not returned by Friday, 28 October.
The Electoral Office has said that if an election is called it would be expected to happen on 15 December.
Paul Givan was speaking after parties met the head of the NI Civil Service.
He said his party wanted to see the institutions back up and running, but it would not re-enter government until changes are made to the Northern Ireland Protocol.
The Stormont Executive has not fully functioned since February, when the Democratic Unionist Party (DUP) pulled its first minister out of office in protest over the Northern Ireland Protocol.
The last assembly election took place on 5 May and saw Sinn Féin returned as the largest party for the first time.
After the May election, the DUP returned as the second-largest party and refused to re-enter government, saying that would remain its position until the UK government acted to change post-Brexit trade arrangements for Northern Ireland.
Talks have resumed between the UK and EU but there is no sign of an imminent deal, with Prime Minister Liz Truss’s own future in peril as she fights to retain control of the Conservative Party.
Image source, PA Media
Speaking after meeting Stormont’s top civil servant, Jayne Brady, on Thursday, Mr Givan said chaos at Westminster was “contaminating the politics of trying to get a deal with the EU”.
He said it was “not for the DUP to get the government off the hook” and insisted his party would welcome another assembly election.
“But will it solve the problems? No, it won’t,” he added.
‘Window of opportunity closed’
Sinn Féin’s vice-president Michelle O’Neill said it “looks like we’re headed” towards another election.
She criticised that and said the situation facing Stormont departments in the coming days would be “bleak”, assuming an executive was not restored.
“It’s madness – I regret the fact that people here are being held to ransom,” she said.
Alliance leader Naomi Long said she believed the “window of opportunity” to restore power-sharing before 28 October had closed.
She added that she had put it to the DUP that the “onus was on them to get real”.
“They currently have probably the most sympathetic prime minister they’re ever going to have.
“If Liz Truss goes, the next prime minister will probably not be an ERG (European Research Group) sympathetic person,” she said.
“The government is in survival mode and has bigger problems than what’s happening in Northern Ireland right now.”
Image source, NI Executive
Ulster Unionist leader Doug Beattie said there was a clear “elephant in the room” to getting devolution back.
“We’re going to have an election, and it’s chaos at Westminster,” she added.
“The lights are on, but nobody is home, nobody’s leading, nobody’s governing.
“All of that will have an effect on us here.”
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Mr Heaton-Harris said talks on the protocol are continuing with the EU, but that should not prevent the immediate restoration of a Stormont executive.
Another election is expected to cost about £6.5m and would have to come from funding already provided to Stormont, according to Northern Ireland’s chief electoral officer Virginia McVea.
On Wednesday, Mr Heaton-Harris rejected suggestions that another election would not lead to any changes and defended how much it could cost as a “down payment for democracy”.
He insisted elections were “never a waste of time and money”.
Analysis: Outlook uncertain as government chaos continues
While the Conservative Party meltdown consumes Westminster, there is still the not-so-small matter of the ongoing crisis at Stormont.
All signs appear to be pointing towards Chris Heaton-Harris pressing go on another Northern Ireland Assembly election.
But with his own government’s future now in peril, no-one knows how things will look by next Friday’s deadline.
It is not even certain if Mr Heaton-Harris will still be in post by then.
The leaders of the five largest parties at Stormont have been holding regular meetings in recent months with the head of the civil service about the financial situation departments are facing if a decision-making executive is not restored.
In the face of political paralysis it will be her staff who could be left in charge of Stormont’s purse strings.
Last week Finance Minister Conor Murphy warned Stormont was facing a £660m overspend unless action was taken.