Gerry Adams has attempted to dictate terms to Theresa May by telling her that she cannot form a government with the backing of Northern Ireland's Democratic Unionist Party.
The Sinn Fein president said he had told the British Prime Minister "very directly" that she was "in breach of the Good Friday Agreement" by trying to agree a deal with the DUP to support her minority Government in the Commons.
Adams said his party would not take its seats in Westminster or swear an oath to the Queen.
It follows warnings from Sir John Major, the former Prime Minister, that the Government will compromise its impartiality in the province if it enters a confidence-and-supply deal with the DUP at Westminster. The 1998 Good Friday Agreement commits the British and Irish governments to demonstrate "rigorous impartiality" in their dealings with the different political traditions in Northern Ireland.
Adams was speaking hours after No 10 said the Queen would open Parliament on Wednesday and set out May's planned laws in the Queen's Speech.
That will come after the start of the first round of talks about leaving the European Union on Monday.
Adams accused May of playing "fast and loose" with the Good Friday Agreement.
"Any deal that undermines the Good Friday Agreement will be opposed by Sinn Fein and, we would hope, the Irish Government.
"If the institutions are to be put in place they need to be sustainable, viable and properly resourced," he said.
Nigel Dodds, the DUP deputy leader, suggested that any confidence-and-supply deal might not be signed by the time of the Queen's Speech. Sources said it could be signed on Tuesday or Thursday.
This could mean that Brexit talks could begin and Parliament is opened without May being able to agree terms with the DUP to support a minority Conservative government.
With her tally of Conservative MPs reduced to 317 in last week's poll, May needs the backing of the DUP's 10 members to reach the 320 required for a working majority in the House of Commons.
A Tory source said May was "confident" of getting the Queen's Speech through the Commons whether or not a deal was reached with the DUP.
The decision to have it two days later than the scheduled date of June 19 was made after May's regular audience with the Queen on Wednesday.