Delegations from Sinn Fein and the SDLP have held separate meetings with Taoiseach Bertie Ahern in Dublin.
The SDLP and Sinn Fein have been meeting Bertie Ahern
The two nationalist parties were discussing the forthcoming talks in Scotland aimed at restoring devolution.
After meeting Sinn Fein, Mr Ahern said the party was "resolute about making an effort to get the institutions up and running before November 24".
Mr Adams said it was now "game on" for a power-sharing deal in Northern Ireland.
Mr Ahern said the restoration of the institutions had to be within the terms of the Good Friday Agreement.
"We're going forward resolute in our endeavours to get these institutions up and running by November 24," he said.
"There needs to be a relentless focus on making this opportunity become a reality."
After the meeting, Mr Adams said there were "big expectations" among the public about restoring devolution.
"I can see it in my own constituency. In fairness to the DUP, they do have challenges. They do have problems that they have to address.
"But let's go forward with goodwill and let's go forward to make this happen."
Sinn Fein president Gerry Adams headed a party delegation
SDLP leader Mark Durkan, who led a six-strong delegation to Dublin, said afterwards that Sinn Fein and the DUP must not delay any longer in setting up power-sharing institutions.
"What we really need is to find out if Sinn Fein signed up to a lawful society and the DUP signs up to an inclusive democracy," he said.
"We have to move forward with a sense of purpose."
The British government has laid down 24 November as the deadline for a deal to be reached over the restoration of devolution.
The main parties meet later this week in the Scottish town of St Andrew's for intensive talks.
Meanwhile, at a briefing of reporters in London on Monday, Prime Minister Tony Blair's official spokesman said there was "a real opportunity" this week to agree the terms for a final settlement in Northern Ireland.
He urged all parties to seize the opportunity presented by Wednesday's talks which, he warned, might not be repeated for the foreseeable future.
The spokesman made it clear that Downing Street believes that a settlement agreed this week could be finalised in time for the 24 November deadline.
"There is a window here to reach a final settlement, and the significance of that cannot be overstated," he said.