Sinn Fein, SDLP and the cross-community Alliance have all also already made clear that Northern Ireland Secretary James Brokenshire can not chair the ongoing process to restore power-sharing at Stormont due to a perceived conflict of interest caused by the deal.
She has already held talks with the DUP this week about a deal to support her minority Conservative government. "We want to govern ourselves".
It could also delay the start of Brexit talks.
Mrs May stressed that Brexit would happen and the timetable remains on course.
During the appearance, Ms O'Neill said: 'We made very clear to the prime minister that any deal between herself and the DUP can not undermine the Good Friday agreement.
"We have just finished a meeting with the British prime minister and her secretary of state, and we told her very directly that she was in breach of the Good Friday agreement", said Mr Adams, speaking from Downing Street.
DUP deputy leader Nigel Dodds, in Downing Street for talks with Mrs May on restoring powersharing in Northern Ireland, refused to be drawn on how the negotiations were progressing.
Sinn Fein, the SDLP and Alliance have all made clear that Northern Ireland Secretary James Brokenshire can not chair the ongoing process to restore power sharing at Stormont because he has a conflict of interest.
"But time is running short and the parties must come together by the June 29th for the return of a strong voice at Stormont and for a brighter future for everyone in Northern Ireland".
What's in the deal?
Colum Eastwood, the leader of the nationalist SDLP, said the government needed to "prove to the rest of us that they are not under the thumb of the DUP".
However, Sinn Fein MPs have never taken their seats in Westminster.
Other legacy matters, such as protecting former soldiers or police officers from prosecution, may feature at a later stage.
Before travelling to the French capital, Mrs May had been leading the talks with the DUP.
"We will be asking the prime minister to be open with politicians and also with the public", he said.
"The SDLP are clear that any deal struck must not hinder cross-community confidence in our politics".
Devolved government in Northern Ireland broke down in January.
The meetings follow last week's snap election in Britain, when May's Conservatives lost their majority in Parliament.
But they added that the London tower block fire made an announcement on Wednesday "inappropriate".
A Conservative source said "broad agreement on the principles of the Queen's Speech" had been reached between the two parties.