The new date for the event, which will feature the Queen's Speech setting out the Government's legislative programme for the coming year, was announced by Leader of the Commons Andrea Leadsom.
Talks with the DUP broke up on Tuesday night without an agreement, but Mrs May said the discussions had been "productive".
The Orange Lodge of Portadown, a fraternal order of anti-Catholics that counts among its members David Simpson, one of the DUP's 10 members of Parliament, issued a statement over the weekend calling on the party to use its leverage with the prime minister to get her to permit its annual parade to once again pass through Catholic areas.
Detractors of the pact include former Conservative prime minister John Major, who said it risked Westminster's neutrality in an ongoing and fragile process.
Sinn Fein's Gerry Adams turned Mrs May's own slogan against her to brand it "a coalition of chaos", adding: "Any deal which undercuts in any way the process here or the Good Friday Agreement is one which has to be opposed".
The Tories and the DUP are considering a "confidence and supply" arrangement which would see the Northern Irish party back the Government to get its Budget through and on confidence motions.
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.
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That concern is made more pressing by two factors: the looming threat of Brexit, which could make it necessary to once again erect barriers along the now invisible border between Northern Ireland and Ireland, once the United Kingdom leaves the European Union; and the fact that Northern Ireland's local assembly is in crisis.
"There is very little time left".
"The power-sharing institutions collapsed because of the DUP's RHI financial scandal and the refusal of previous Tory governments and the DUP to implement previous agreements".
It is thought Mrs Foster, despite being a Brexit supporter, could seek assurances from Mrs May that she will pursue a softer exit from the European Union, given Northern Ireland's 56% Remain vote and the DUP's desire not to see a return to a hard border with Ireland.
However, the announcement of the deal was postponed on Wednesday because of the Grenfell Tower fire disaster.
"Progress will not come from a deal between the DUP and Tories to prop up a government in Westminster with an austerity and Brexit agenda but through the full implementation of the agreements and an Executive that respects the rights and delivers for all in society".
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