Dodds will meet May at Downing Street on Thursday afternoon for one of a series of meetings May is having with the leaders of Northern Ireland parties in an effort to reach agreement on setting up a new power-sharing government for the region, he said.
Sinn Fein, the SDLP and Alliance have also insisted Mr Brokenshire can not be an impartial chairman of the talks to restore the Stormont power-sharing institutions because of the DUP/Tory link-up.
"We continue to work with all the parties in Northern Ireland and the Republic of Ireland in ensuring that we can continue to put in place those measures necessary to fulfil those agreements, " she said.
But he warned against James Brokenshire being brought in as a mediator to the negotiations, saying he represents the "partisan" British Government.
"The UK Government is offering whatever support we can, working alongside the Irish government, as appropriate, honouring our respective commitments in the Belfast Agreement to serve the interests of the whole community in Northern Ireland", he said.
The meeting comes after Irish nationalists voiced concerns that a planned deal between May's Conservative Party and Sinn Fein's unionist rival the Democratic Unionist Party (DUP) could destabilize politics in Northern Ireland.
DUP leader Arlene Foster has told Sinn Fein leaders if they are concerned about her party's enhanced influence at Westminster they should move to restore devolution at Stormont.
Negotiations broke up on Tuesday night without an agreement, but Mrs May said the discussions had been "productive".
The proposed deal would see the DUP back the Conservatives in votes on the Budget and confidence motions.
The Secretary of State said the Government remained "four square" behind the Good Friday deal.
"It's imperative that both Governments recommit to the word, spirit and implementation of the Good Friday Agreement if there is to be any prospect of re-establishing the Executive".
May took up her familiar refrain, arguing the deal is vital to "give the stability to the UK Government that I think is necessary at this time".
It follows warnings - including from former prime minister Sir John Major - that the Government will compromise its stated impartiality in the province if it enters a confidence and supply deal with the DUP at Westminster.