Brexit: DUP criticises May's 'lamentable' negotiations
The DUP has called the prime minister's handling of the overall Brexit negotiations "lamentable".
The party's criticism comes after Theresa May said on Tuesday that she is to ask the EU for a further extension to Brexit.
Mrs May also said she has called on Jeremy Corbyn to meet her to find a compromise.
Sir Jeffrey Donaldson said events at Westminster were still a "moveable feast".
The DUP MP told BBC Radio Ulster regardless of what emerges in the coming days, the DUP's stance on the union was "un-persuadable" and they remained in an "influential position" because of the government's fragile working majority in Parliament.
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The party said that Mrs May's plans would be "sub-contracting" the future of Brexit to Mr Corbyn.
The DUP's Brexit spokesman Sammy Wilson told BBC News NI his party had not been "sidestepped" and that he suspected the negotiation will "fall on its face just as everything else she has tried to do in the past has fallen on its face".
Mr Corbyn said he was "very happy" to meet Mrs May, and would ensure plans for a customs union and protection of workers' rights were on the table.
Sinn Féin said Parliament could not keep talking to itself about "fantasy options" not on the table.
The DUP has supported the government in a confidence-and-supply pact since June 2017, after a snap general election.
But it is at odds with Theresa May and her Brexit deal, because of the Irish border backstop in the withdrawal agreement.
It opposes the plan because if it took effect, it would lead to trade differences between NI and Great Britain, which the DUP said poses a risk to the integrity of the union.
On Tuesday evening, after Mrs May gave a speech setting out her plan for the days ahead, the DUP said it would remain "consistent" in judging all Brexit outcomes against its unionist principles.
The party added that: "It remains to be seen if sub-contracting out the future of Brexit to Jeremy Corbyn, someone whom the Conservatives have demonised for four years, will end happily."
Sinn Féin said Mrs May could not request another extension from the EU without a clear reason.
"We are now 10 days away from a potential crash-out Brexit and it is clear the British government and Parliament has no plan, no strategy and no clue what it is doing," said its Foyle MP, Elisha McCallion.
SDLP leader Colum Eastwood said he was "glad Theresa May has decided to ditch the ERG and DUP version of Brexit".
Taoiseach Leo Varadkar held talks with French President Emmanuel Macron, on Tuesday and said the EU needed to consider any proposals the UK brought forward in the coming days.
The UK is still scheduled to leave the EU on 12 April, unless the EU agrees to another extension.
But it is likely to demand that the UK takes part in European elections, which are due to take place on 23 May.
However, Mrs May said she wanted any further extension to be "as short as possible" - before 22 May so the UK does not have to take part in the elections.
Both the UK and EU have continued preparations for no deal, in the event that a breakthrough cannot be reached in time.