Britain's Prime Minister Theresa May File picture: Matt Dunham/AP

Dublin - The head of the Northern Irish party that props up British Prime Minister Theresa May's government said on Thursday its 10 members of parliament would vote against her Brexit divorce deal and had never considered abstaining.

In a serious blow for May, the Democratic Unionist Party (DUP) announced on Wednesday it would not support her deal. A leading Brexiteer in May’s Conservative Party, Jacob Rees-Mogg, had earlier suggested some critics of the divorce deal might back it if the DUP agreed to abstain.

"You cannot abstain on the union. You just could not do that," DUP leader Arlene Foster told Irish state broadcaster RTE in an interview, referring to the union between Northern Ireland and Great Britain.

"Abstention would be the worst of all worlds because you are not actually indicating where you stand on the most important issue of our times so that was never an option," she said.

Asked if the DUP might support a "softer" alternative Brexit deal that maintained closer ties between Britain and the European Union, Foster said the most important thing for the party was that Northern Ireland was not treated differently from the rest of the United Kingdom.

"We want to see Brexit delivered. But if it's a Brexit that keeps the whole of the United Kingdom together, that is the most important thing," she said.

In a last-ditch attempt to win the support of eurosceptic rebels in her party, May said on Wednesday she would quit as prime minister if her Brexit deal were finally approved by parliament at a third attempt.