She made no comment as she left 10 Downing Street en route for the House of Commons. The Conservatives are considering an arrangement in which the Northern Ireland party backs May on the budget and her confidence motions and the DUP stands to make huge gains from the deal.
"She said: "I'm the person who got us into this mess and I'm the one who is going to get us out of it", said one Conservative lawmaker who attended Monday's meeting.
On Brexit, Ms Foster said her party wanted to see "a sensible Brexit and one that works for everybody".
Colum Eastwood, leader of the SDLP, Northern Ireland's second-largest Irish nationalist party, said his party had a "positive" meeting with the prime minister over her efforts to come up with a deal with the DUP.
Britain entered a sixth day of political limbo on Wednesday with Prime MinisterTheresa May yet to seal a deal to prop up her minority government and facing calls to soften her stance on Brexit days before negotiations on leaving the European Union begin.
He thinks it risks violence returning to Northern Ireland.
Conservative chief whip Gavin Williamson flew to Belfast on Saturday to begin formal discussions with the DUP after the election resulted in a hung parliament.
The Democratic Unionist Party wants to attach its own conditions onto Brexit as part of its deal with the Conservatives - including the insistence on a "soft border" between Northern Ireland and the Irish Republic.
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Takulua and Davies exchanged further kicks at goal, but the error count was high as kicking dominated the game. Takalua was then unable to find the mark with a kick of his own and with that, the game was up.
Though Foster supported Brexit, she also might demand that May pursue a cushioned exit from the European Union, given her party's wish that a soft border remain between Northern Ireland and Ireland, an European Union member.
"The British government has said we will stay with the Brexit".
She said the DUP's negotiations with British Prime Minister Theresa May and the Conservative Party would continue through the weekend and next week.
The draft law would empower Europe to decide if post-Brexit London has the right to host financial market "clearing houses" that deal in euros, the EU's single currency.
The Chancellor had been due to use a high-profile speech in the City of London on Thursday night to send out a message the Government would protect business from shocks during the Brexit process. When asked about the Daily Telegraph article, Michael Gove, a minister who campaigned for Brexit, told ITV: "This is news to me".
It follows warnings - including from former prime ministerSir John Major - that the Government will compromise its stated impartiality in the province if it enters a confidence and supply deal with the DUP at Westminster.
"My clear view, and I believe the view of the majority of people in Britain, is that we should prioritise protecting jobs, protecting economic growth, protecting prosperity as we enter those negotiations and take them forward", Hammond said."As we enter negotiations next week, we will do so in a spirit of cooperation, taking a pragmatic approach, trying to find a solution that works both for the United Kingdom and the European Union 27", he told reporters before a meeting of the 28 EU finance ministers in Luxembourg.
But May faces a hard balancing act: Divisions over Europe helped sink the premierships of Margaret Thatcher, John Major and David Cameron, and many of her lawmakers and party membership support a sharp break with the EU.
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