The Minister for Justice, Mr McDowell, this evening dismissed an attack on him by the Sinn Féin leader, saying Mr Adams remarks were "the product of tiredness".
Earlier, Mr Adams said he had no confidence in Mr McDowell's ability as a negotiator with the British government and unionists.
In a fierce attack, Mr Adams said Mr McDowell's description of his Government as an "honest broker" in the process was wrong. He said Dublin was an equal partner and should be upholding the right of Irish citizens.
"It is little wonder that the British government is so dismissive of the views of both the Taoiseach and all parties on the island with the exception of the UUP, given Mr McDowell's explanation of the Irish Government's role," he said.
Mr Adams said it was obvious from the Taoiseach's remarks that he did not agree with the suspension of the elections that the British government was calling the shots in the process.
"I don't expect the unionist political leadership to behave in any other way. It wasn't David Trimble who cancelled the election. He didn't take the decision. It was taken by Mr Blair and he disregarded the wishes of everyone else".
Mr Adams added that Mr McDowell had no affinity with nationalists or republicans.
He said it was little wonder that the British government had ignored the views of Dublin. "I wouldn't send Michael McDowell to the shop for a bottle of milk if this is the way he perceives the role of the sovereign government in Dublin. It is a nonsense".
When it was put to Mr McDowell that Republicans felt betrayed by the Government, he said this could not be the case.
"We have done our level bestto bring about a situation in which the acts of completion which were required by the two Prime Ministers in their statement last November. We have put a huge amount of effort into mapping the way forward," he said.
As the rift deepened, Tánaiste Ms Mary Harney, defended her the Government's role in the peace process.
Ms Harney was on a visit to Derry when she was confronted by Sinn Féin supporters angry at yesterday's events.
She said the Government would remain focused on working to restore the devolved institutions in Northern Ireland.
"Nobody has worked harder to defend this Agreement than the Irish government," she told reporters.
"The Irish government was instrumental with the British government and the parties in Northern Ireland in negotiating the Good Friday Agreement," she added.
A Government spokesperson expressed surprise at the tone of Mr Adams's outburst.
He said Mr McDowell had made it clear that the two governments were working together to further the peace process.
"He also made it quite clear that the Irish Government would have preferred elections. He didn't differ from what the Taoiseach was saying," he added.
Meanwhile Mr Adams called on people to demonstrate their opposition to the suspension of the election at a rally to commemorate the hunger strikes in West Belfast on Sunday and to peacefully demonstrate on the streets on May 29th - the date when the elections should have gone ahead.
SDLP leader Mr Mark Durkan claimed the British and Irish governments' Joint Declaration published yesterday had totally vindicated his party's stance on policing.
"The SDLP at Hillsborough also won far-reaching changes to criminal justice. We look forward to their publication in the revised Criminal Justice Implementation Plan," he added.
"I am calling on Tony Blair and Bertie Ahern to now make clear the status of the Joint Declaration.
"The SDLP wants to see it implemented. Neither the IRA nor unionists can have a veto on its implementation. Nor should IRA activity or unionist intransigence be used as an excuse by the British government for not implementing it."
After the publication of the two government's Joint Declaration yesterday, theIRA remained under pressure to release its proposals on advancing the peaceprocess.
The confidential IRA statement sent to the British and Irish governments three weeks ago was expected to be published early next week.
Before that, republican supporters were expected to vent their opposition tothe postponement of the election at a rally in west Belfast on Sunday tocommemorate the death of IRA hunger striker Bobby Sands.