O'Neill said she will also travel to Dublin in the coming days to meet with new Irish Prime Minister Leo Varadkar.
A Conservative source said this meant the party was "confident" it had enough votes for the programme to be approved, after May suffered a disastrous setback in snap elections a week ago that saw her lose her majority in the 650-seat House of Commons, just ahead of crucial Brexit negotiations with Brussels.
Mr Adams said the republican party is ready to do business with the DUP and the other main political parties in a bid to salvage devolution.
SDLP leader Colum Eastwood warned that the future of Northern Ireland could not be left "in the hands of a Tory-DUP government".
The DUP represents people in Northern Ireland who wish the province to remain part of the United Kingdom, while Sinn Fein wants Northern Ireland to be administered by the Irish Republic.
Theresa May is to hold talks with the Northern Ireland political parties amid warnings an expected deal with the Democratic Unionists (DUP) to prop up her minority government will undermine the peace process.
The DUP have been playing their cards close to their chest, but we know the areas they're talking about because of a DUP plan drawn up in 2015 in anticipation of a hung Parliament.
"We are today calling on the next UK Government to commit, particularly in the absence of functioning devolution, to prioritise bringing Northern Ireland's abortion laws in line with worldwide human rights standards".
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He claimed such a deal could endanger the peace process.
It comes as Theresa May faces a showdown over the DUP deal with the Sinn Fein president Gerry Adams in Downing Street this afternoon.
Sinn Fein, which won seven seats in the British parliament at last week's election but will maintain its policy of not taking them, said its leader in Northern Ireland, Michelle, O'Neill would repeat those concerns in London on Thursday.
"Bringing stability to the United Kingdom government in and around issues around Brexit, obviously around counter-terrorism, and then doing what's right for Northern Ireland in respect of economic matters".
But the other Stormont parties have warned that any deal between the DUP and Conservatives could make restoring power sharing more hard.
Northern Ireland has been without a powersharing executive since March and without a first and deputy first minister since January.
"If they cease to be seen as an honest broker than we can not be certain how events will unwind".
It has always been speculated that such an agreement would leave the government in breach of its duties under the Nothern Irish power sharing arrangement, signed on Good Friday in 1998.
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