DUP sources have told the BBC an announcement on a deal with the Conservatives has been delayed because of the Grenfell Tower blaze.
The two sides were close to reaching agreement to enable Theresa May to form a minority government and the talks were not in trouble, the sources added.
But they added that the London tower block fire made an announcement on Wednesday “inappropriate”.
And diary commitments meant a final deal could be delayed until next week.
The DUP source told BBC assistant political editor Norman Smith the two parties were now finalising the “terms and conditions” of an agreement after Mrs May and DUP leader Arlene Foster met on Tuesday.
Downing Street sources told our correspondent talk of a delay in announcing a deal was “not coming from us.”
If a deal was to be delayed it would mean the Queen’s Speech, which had originally been planned for next Monday, could be delayed by at least a week.
It could also delay the start of Brexit talks.
The Conservatives are having to rely on the support of 10 DUP MPs after they fell eight seats short of winning an overall majority at the general election.
It means that Mrs May will remain as prime minister and the DUP MPs will be central to the survival of a Conservative Party administration.
What’s in the deal?
By BBC Northern Ireland political editor Mark Devenport
The DUP have been playing their cards close to their chest, but we know the areas they’re talking about because of a DUP plan drawn up in 2015 in anticipation of a hung Parliament.
Things have moved on a bit since then with Brexit, but we do know they’re looking at trying to lower the cost to the Northern Ireland executive of any move on corporation tax.
They’ve been of the view that leaving the EU should lessen some of the stipulations in relation to state aid that were being applied by the Treasury to Northern Ireland, and that might take down the bill that the Treasury would put on the executive if corporation tax was lowered.
We know other matters, such as cutting air passenger duty and increased infrastructure spending, have been discussed, but we haven’t got any sense of the exact details of the deal.
I suspect it will be top loaded with economic rather than political matters.
Some political issues, such as altering the definition of a Troubles victim or doing away with allowances for MPs who don’t take up their seats, might be included.
Other legacy matters, such as protecting former soldiers or police officers from prosecution, may feature at a later stage.
The DUP will offer support for key votes, such as backing the Queen’s Speech and the Budget and opposing any votes of no confidence.
The DUP campaigned for Brexit but is also conscious that 56% of people in Northern Ireland voted to remain in the EU.
They are thought to be advocating a Brexit that does not disrupt the “frictionless border” with the Republic of Ireland.
They are also opposed to Conservative polices such as means-testing the winter fuel allowance and have campaigned for a higher National Living Wage and to restore the spare room subsidy.
The party is also likely to push for more investment in Northern Ireland, with emphasis on increased borrowing powers and looser budget controls rather than direct cash.
Prime Minister Theresa May said on Tuesday that talks with the DUP had been productive and that Brexit negotiations would begin as planned next week.
“I think there is a unity of purpose among people in the United Kingdom,” Mrs May said, following a meeting with French President Emmanuel Macron in Paris.
The agreement with the DUP is expected to be very different from the coalition deal agreed between the Conservatives and Lib Dems in 2010, with DUP politicians not getting cabinet jobs and their support for the majority of new legislation to be determined on a vote-by-vote basis.
Labour’s shadow business secretary Rebecca Long-Bailey called it a “very dangerous deal” and said Labour was “ready and waiting to form a minority government”.
She dismissed accusations of hypocrisy after it emerged then Labour leader Gordon Brown had tried to do a deal with the DUP in 2010, telling BBC Radio 4’s Today programme: “It’s certainly not something that [current Labour leader] Jeremy [Corbyn] would advocate, and the Labour Party is certainly not advocating that.
“As I’ve said, it would create a lot of instability in terms of the peace process in Northern Ireland and it’s a very worrying time.
“It just illustrates the chaos that the Conservative Party are in at the moment.”
On Tuesday, ex-Conservative Prime Minister Sir John Major said he was “dubious” about the idea of a deal and its potential impact on the peace process.
Sir John told BBC Radio 4’s World at One programme there was a danger the government would no longer be seen as an “impartial honest broker” in restoring the power-sharing arrangements and upholding Northern Ireland institutions.
Asked about Sir John’s comments, Mrs May said she was “absolutely steadfast” in her support for the 1998 Good Friday agreement – which created the Northern Ireland Assembly – and efforts to revive the power-sharing executive.