Talks between the Taoiseach, Bertie Ahern, and the Green Party leader, Trevor Sargent, on a possible coalition deal have adjourned for the night.
There will be further contact between the two sides tomorrow.
Speaking afterwards, the Minister for Social and Family Affairs, Seamus Brennan, said good progress had been made and if the same level were achieved tomorrow there would be a deal for government.
It is understood the Green Party now hopes to re-schedule a special conference in the event of an agreement for Wednesday night, the eve of the Dáil voting for a new Taoiseach.
Tonight's talks, which broke up just after 9pm, came after a day of contacts between the parties to discuss the difficulties which led to the collapse of coalition talks last Friday.
In another development, Independent TD Jackie Healy-Rae has signed an agreement with Mr Ahern to support him in the vote for Taoiseach on Thursday and to support his government for the next five years if he is elected.
The Kerry South TD said he had agreed a package worth tens of millions which will be invested in health care, district hospitals, and roads in Co Kerry over the next five years.
Deputy Healy-Rae said the package significantly surpassed what he had secured in return for his support in 1997.
Earlier, Mr Sargent said the work should not be dictated by deadlines but that time was clearly getting short if they were to call a convention of party members before the Dáil meets on Thursday.
The Minister for Finance, Brian Cowen, said earlier this evening that he believed a fair offer had been made.
Green Party negotiator Dan Boyle also said progress had been made on a number of issues, but that a number of problems remained.
Speaking on RTÉ Radio's Drivetime, Mr Boyle said his party would have to make a decision this teatime on whether to call a conference of its membership to discuss entering government but first there would have to be agreement on some of the substantial issues.
Mr Boyle said Mr Ahern and Mr Sargent had been in contact by phone to assess the process but had not been tic-tacing during the day.
Earlier, Mr Sargent said the difficulties which caused the collapse of talks last Friday still remained, but he said he hoped they could be 'ironed out'.
Mr Sargent said his party was still examining Fianna Fáil's response to the GP document, which outlined problem areas in the talks. But he said the difficulties may not be as 'insurmountable' as Fianna Fáil had thought.
He said calling a convention before Thursday would be a 'logistical nightmare', but if they had to do it they would, although he stressed that time was running out.
With or without the Greens' support, it is now widely expected that Mr Ahern will be elected Taoiseach on Thursday with backing from the Progressive Democrats and some of the Independents.
There is also speculation that Fianna Fáil would seek a Ceann Comhairle from the Opposition benches in order to strengthen its majority.