Michelle O'Neill, Sinn Fein's leader in Northern Ireland, said an agreement between May and the Democratic Unionist Party's 10 MPs in the London parliament to prop up her minority government was at fault.
"She is in hock to the DUP," O'Neill told reporters in Belfast in comments aired on national television.
Marathon talks to form a new power-sharing executive in Northern Ireland with Sinn Fein and the DUP were delayed yet again after the parties admitted they could not reach a deal before the summer recess.
"She has set back decades of work," O'Neill said.
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Conservative leader May was forced to strike a deal with the ultra-conservative DUP last month after losing her majority in a June 8 general election.
The British government has insisted that the deal has no bearing on the Northern Ireland peace process.
DUP leader Arlene Foster told a news conference in Belfast: "We are disappointed we don't have an agreement this afternoon... Hopefully we can come to an agreement later on in the year."
Britain and Ireland are co-guarantors of the process.
Northern Ireland's executive collapsed in January when Sinn Fein demanded DUP leader Arlene Foster step aside pending a public inquiry over a botched green energy scheme and accusations of "arrogance" towards Irish nationalists.
Foster has refused to stand down.
Britain's Northern Ireland Secretary James Brokenshire warned on Monday that if no agreement was reached he would be forced to draft a budget for the province and have it enacted by civil servants.
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