Any extra money for Northern Ireland under a Conservative-DUP deal at Westminster should also lead to more cash for Wales, say Welsh ministers. 'We hope soon to be able to bring this work to a successful conclusion'.
"We want to see an administration set up again that will last and one that will last for all of the people of Northern Ireland", said Ms Foster outside Dublin's Government Buildings.
Former British Prime Minister John Major said he was concerned May's plan to govern with the support of the DUP could pitch the province back into turmoil by persuading "hard men" on both sides of the divide to return to violence.
With formal European Union divorce talks due next week, May heads to France on Tuesday, possibly to bask in the popularity of Emmanuel Macron, who last month swept to victory in a presidential contest. Foster said on Twitter. "I can't negotiate with myself", he told The Financial Times.
Major pleads with May to reject a deal and form a minority government instead.More news: Senate approves new Russia sanctions
Arlene Foster flew out to London on Monday to hold talks in Downing Street.
She told the influential 1922 Committee of backbench MPs that she had got the party into "this mess" by calling the snap election, but she would "get us out of it".
But any deal between the DUP and the Tories could worsen tension in Northern Ireland and open the door to a referendum on unity with Ireland.
But a deal with the DUP also risks destabilising Northern Ireland by increasing the influence of pro- British unionists, who have struggled for years with nationalists.More news: Champions Trophy: India, Pak gear up for 'mother of all finals'
Meanwhile, the chief European Union negotiator has told the Financial Times that the clock is ticking on Brexit talks, and that Britain should be wary of further delays.
So we are very, very positive, and I hope that Her Majesty's Loyal Opposition on this issue - when our Prime Minister is in Brussels arguing for the whole country - that they understand they said they wanted the same things and that's what she's trying to deliver.
"We are united in our total condemnation of terrorism and our commitment to stamp out this evil", May said ahead of her visit.
Brexit negotiations that were scheduled to begin next week was also likely to be postponed.
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).More news: Representative Scalise's condition upgraded to 'serious' after shooting
- 58 presumed dead in London tower blaze, police say
- London highrise fire: 58 missing, presumed dead, police say
- Defending champion Johnson out of US Open
- Obamas invited to be honorary football coach at University of MI
- Wales wing Alex Cuthbert out of Samoa clash with shoulder ligament damage
- Kershaw wins, Bellinger hits 2 homers as Dodgers top Indians
- Islamabad says two Pakistani diplomats have gone missing in Afghanistan
- We need worldwide co-operation on climate change, says Gove in Trump attack
- Champions Trophy final: Players look within before big game
- Grenfell Tower fire: Protests as anger grows