It is still unclear if she has locked in the support of the Northern Irish DUP to prop her up in the House of Commons and give her the majority she needs to pass a vote approving the agenda set out in the Queen's Speech.
Scottish Conservative leader Ruth Davidson said the government should put economic growth at the heart of its Brexit strategy, comments placing her in the camp of those advocating a closer trade relationship with the European Union, or "soft" Brexit.
Arlene Foster appeared to hint at this when on Tuesday she spoke of counter-terrorism and Brexit as having featured in the negotiations.
"Nigel Dodds says he won't commit to any deadline and talks will continue until DUP and Conservatives get right deal", BBC Northern Ireland correspondent Mark Davenport said in a tweet.
While she is ultimately expected to reach a deal, a source in the Democratic Unionist Party (DUP) told Reuters that an agreement to support her minority government was not likely before next week. Britain will leave the European Union on March 29, 2019 - unless she calls to reverse it and the 27 other European Union member states vote unanimously to allow her to do so.
"If the Government cannot even secure a deal with the DUP, how on earth can they get a deal with the EU?"
But pressure was mounting for May to change course on the type of Brexit Britain should pursue.
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The meeting between Foster and Varadkar highlighted issues that have made some British politicians wary of a deal with the DUP.
The talks were "productive", May told a news conference in Paris following a meeting with French President Emmanuel Macron.
Besides forging a deal to keep her job and preparing for Brexit talks, May is also grappling with a crisis over the breakdown in power-sharing between the pro-British DUP and the Catholic nationalist Sinn Fein party in Northern Ireland's separate, devolved government.
British negotiators believe the European Union might accept such a deal because it would mean Europe's trade in goods with the United Kingdom - in which the European Union runs a surplus - would not be disrupted by Brexit, the newspaper said.
"We would restore faith in politics if we could show that this parliament can at least function in presenting a view in the national interest which would command a majority on a cross-party basis", said veteran pro-European Conservative lawmaker Ken Clarke.
Sinn Féin Leader in the north, Michelle O'Neill, insisted that any DUP-Tory arrangement should not be allowed to undermine the peace process.
While the DUP are deeply eurosceptic, they have baulked at the potential loss of a "frictionless border" with the Republic of Ireland.
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