May desperately needs the Democratic Unionist Party's 10 seats to pass legislation.
The DUP has blocked all progress on equal marriage in Northern Ireland, and supports the introduction of a "conscience clause" to protect people who discriminate against LGBT people.
"What we're doing in relation to the talks that we're holding, the productive talks we're holding with the Democratic Unionist Party, is ensuring that it is possible to, with their support, give the stability to the United Kingdom government that I think is necessary at this time", May told a news conference in Paris following a meeting with French President Emmanuel Macron.
British officials held "talks about talks" with the European Union's Brexit man in Brussels but actual negotiations, scheduled to start in a week's time, might be delayed by political upheaval in London.
Party leader Arlene Foster seemed buoyant as she arrived at May's Downing Street office and her happy mood continued even after May left for the House of Commons without comment. The Evening Standard, edited by ex-Treasury chief George Osborne, reported that Cabinet ministers have initiated talks with Labour lawmakers to come up with a "softer", less hard-line divorce from the EU.
May also restored former Justice Secretary Michael Gove to the Cabinet in another move created to show she was willing to listen to critics.
'It's going to be hard, there's no doubt about that, but perhaps an opportunity to consult more widely with the other parties on how best we can achieve it, ' Cameron was reported by the FT as saying at a conference in Poland on Tuesday.
The initiative restarted on Monday, after breaking for the General Election, but negotiations have again been put on ice on Tuesday as the political focus shifted to Westminster and the anticipated parliamentary deal between the DUP and the Conservatives.
Authorities: 14 people go to hospital after deck collapse near Flathead Lake
Glacier Camp is a Presbyterian summer camp near Lakeside, on the northwest side of Flathead Lake in Glacier National Park. The department says it doesn't believe the county has regulations on the maximum capacity of balconies or decks.
John O'Doherty, of LGBT health group the Rainbow Project, said: 'It is time for government to respect the will of the people of Northern Ireland, which is overwhelmingly in support of civil marriage equality.
The former prime minister, who began work engaging with the IRA to end the Northern Ireland conflict, said the peace process was still "fragile" and cautioned the pact could mean the Government will no longer be seen as impartial.
She reiterated that any deal between her party with the Conservatives was not bad news for devolution in Northern Ireland.
Speaking at Leinster House, the Sinn Féin leader, Gerry Adams, made a stinging attack on the prospect of an agreement between the Conservatives and the DUP.
He said he was "concerned" about the deal between the two parties, and saying he was "wary" and "dubious" about it "both for peace process reasons but also for others reasons as well".
Speaking straight after a meeting with DUP leader Arlene Foster, the Prime Minister praised the increased diversity in the chamber, noting the record number of LGB MPs as well as the record number of BME MPs, disabled MPs and female MPs.
"If that's not possible, the Labour Party stands ready to offer strong and stable leadership in the national interest".
Meanwhile, the chief European Union negotiator has told the Financial Times that Britain that the clock was ticking on Brexit talks, and that Britain should be wary of further delays.