Although the DUP are unionists - wanting to remain part of the United Kingdom - and broadly support numerous policies of the Conservative and Unionist Party (as the Conservatives are correctly called), May's proposed deal could scupper attempt to broker a power-sharing deal with Sinn Fein - which promotes the unification of Ireland - on the Northern Ireland Executive.
"The Queen's Speech is not the be all and end all in relation to the negotiations that we have been having with the Conservative Party but I do hope that in the national interest we are able to conclude these talks as quickly as possible" Foster told BBC in an interview.
"People knew that we were abstentionist MPs, they have elected us to represent them but not to take our seats".
London's neutrality is key to the delicate balance of power in Northern Ireland, which was once plagued by violence over Britain's control of the province.
Conservative former Prime Minister Sir John Major, who was crucial in bringing peace to Northern Ireland, has raised concerns about the impact of a Tory deal with the DUP.
May apologised to Conservative MPs on Monday, accepting personal responsibility for failing to win an outright victory and sacrificing the parliamentary majority she inherited from her predecessor David Cameron when she came to power a year ago following the UK's vote to exit the European Union (EU).
Arrest warrants out for Turkish agents in DC melee
Alpkenan Dereci, who was seen on video punching and shoving a protester, has not been charged with any offence. The New York Times notes that this isn't the first time Erdogan's security detail has misbehaved on USA soil.
The pro-Brexit DUP nevertheless wants no return to a Border and customs controls between north and south and wants continued access to the European Union single market.
Northern Ireland's frontier with the Republic of Ireland will be the UK's only land border with the European Union after Brexit.
As May attempts to cobble together a majority, the EU's chief Brexit negotiator Michel Barnier warned that time was passing in an interview on Tuesday.
"We are working on a series of fronts and we are working very, very hard to deliver good government for Northern Ireland and good government for the United Kingdom", he said. "I can't negotiate with myself", he told The Financial Times.
As he arrived at the Dail in Dublin ahead of Enda Kenny's formal resignation as taoiseach, Mr Adams said incoming Irish premier Leo Varadkar needed to put his efforts into restoring powersharing north of the border. As usual, Scotland's First Minister Nicola Sturgeon is calling for more nationwide involvement in the actual Brexit talks.