"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 after the meeting.
The Prime Minister is to hold talks with political leaders from Northern Ireland in a bid to allay fears the anticipated parliamentary deal with the Democratic Unionists will undermine the peace process.
May does not necessarily need a firm deal from the DUP before opening parliament and might hope that she would receive the necessary backing anyway.
The move comes amid concerns the Government will compromise its stated impartiality in the region if it enters a confidence and supply deal with the DUP at Westminster.
Though on the surface, Thursday's meeting with Northern Irish parties is aimed at breaking the logjam in forming a new cross-party regional government in the province, May needs broader acceptance of a Conservative-DUP deal.
Founded in 1971, the Belfast-based DUP has always been a strong advocate of Northern Ireland remaining part of the UK.
"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".
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.
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Sinn Fein, the SDLP and Alliance have all said that the Tory Northern Ireland Secretary James Brokenshire can not continue to chair talks aimed at resuming powersharing at Stormont.
Northern Ireland remained part of the United Kingdom when the rest of Ireland gained independence from Britain in 1922, and border controls largely melted away in the 1990s. "They want a frictionless border but at the same time hint they want to leave the customs union, which is not a very consistent position".
He stressed the objectives of ensuring that Brexit does not impact negatively on the Good Friday Agreement and the peace process there, and protecting North-South trade and economic activity and the Common Travel Area.
Of course he is now concerned with his peace process legacy, but the warnings he sounded during the week about the dangers to Northern Ireland as a result of the British general election and the DUP holding the balance of power should be taken seriously.
Brexit is another complicating factor in the mix.
London, Belfast, Dublin and Brussels all want to keep the border open, but no agreement has been reached.
"She doesn't have a mandate for scrapping the winter fuel allowance, or taking hot meals away from children, and there could be support for other things too, such as scrapping the bedroom tax", the source said.
"This will continue as long as no one is able to find a workable solution for the border issue".