"The UK government is offering whatever support we can, working alongside the Irish government, as appropriate, honouring our respective commitments in the Belfast Agreement to serve the interests of the whole community in Northern Ireland". Ms Foster said she hoped a deal could be done "sooner rather than later".
After losing her parliamentary majority in a botched gamble on a snap election, May's Brexit strategy has become the subject of public debate inside her own party, with calls for her to take a more business-friendly approach.
It follows warnings - including from former prime minister Sir 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.
A senior Conservative Party source agreed.
British Prime Minister Theresa May was scheduled to meet the leader of a small Northern Irish Protestant party on Tuesday to save her premiership and avoid a second election that would thrust Brexit negotiations into turmoil.
The DUP and Sinn Fein are taking part in Thursday's talks at Downing Street, along with smaller parties.
With this eventuality in mind, one of the party's ten Westminster MPs Jim Shannon tried to allay concerns that there will be a hard border between Northern Ireland and the Republic that could hinder trade.
"That is why we're ready to start very quickly".
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May's programme will most probably have to be watered down, dropping some of her preferred reforms to help get legislation through Parliament and possibly having to give way to other ministers who have strong views over the direction of Brexit.
Northern Ireland is now without a government, after a surge in support for Sinn Fein at Northern Irish Assembly elections earlier this year left nationalist parties holding a majority over unionist ones the first time.
During the campaign, May cast herself as the leader to navigate the negotiations that will shape the future of the United Kingdom and its $US2.5 trillion ($A3.3 trillion) economy.
Foster's rivals in Northern Ireland, such as Sinn Fein's Gerry Adams, have objected, describing any partnership between the Conservatives and the DUP as "a coalition of chaos".
May's spokesman said the prime minister, who in March set Britain on a two-year countdown to leaving the EU that included a clean break with the bloc's single market and customs union, was not changing her position on what she wants from Brussels.
Brexit minister David Davis has insisted the approach to the European Union divorce had not changed, but at the meeting with MPs on Monday, May recognised that a broader consensus needed to be built for Brexit and made clear she would listen to all wings of the party on the issue.
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