Negotiators from both sides have reported good progress in talks on Monday evening between Fine Gael and Independent TDs on the formation of a new government, with ministers remaining optimistic that a deal can be agreed in the coming days.

The talks will recommence at Government Buildings on Tuesday morning.

Fine Gael and Fianna Fáil are planning to hold meetings of their parliamentary parties on Tuesday to discuss last week's agreement between the two parties.

It is understood leaders Micheal Martin and Enda Kenny will outline the parameters of the deal to their TDs and seek their approval.

Rural TDs had requested an outline of the joint programme for government agreed by Fine Gael and Fianna Fail ahead of Monday’s meeting.

Independent TD Denis Naughten said he understood the five rural TDs could not see the final document until it has been approved by both parliamentary parties.

However he stressed that he and his colleagues would request details on what was decided between the two parties.

“We want to be sure that issues we raised with Fine Gael at meetings are dealt with in the agreement,” said Mr Naughten. “I don’t believe it is unreasonable to ask for the outline of it.”

Mr Naughten said there is a hunger among the rural TDs to bring these discussions to a speedy conclusion. “There is a willingness to ensure that we do not delay one hour longer than we have to.”

Mr Naughten, Clare TD Michael Harty, Cork South West TD Michael Collins, Tipperary TD Mattie McGrath and Galway West TD Noel Grealish met Fine Gael on Monday evening.

Meanwhile, Roscommon-Galway TD Michael Fitzmaurice said on Monday he would be very surprised if there was a government and Taoiseach in place by Thursday.

Referring to a "guesstimate"on Sunday by Fine Gael negotiator Simon Coveney that a new government could be in place by this Thursday, Mr Fitzmaurice said it was "no good coming out with rash statements. We have to be realistic. That [Thursday]would be pushing it."

The four-person Fine Gael negotiating team resumed talks on a joint programme for government with the Independent Alliance at 10am on Monday.

The Independent Alliance - comprising Shane Ross, Finian McGrath, Kevin "Boxer" Moran, Seán Canney, Michael Fitzmaurice and John Halligan - is being courted by Fine Gael as it bids to secure the 58 votes it needs, if Fianna Fáil abstains. Telephone contact between the sides took place over the weekend.

Fine Gael hopes it can form a government this week with Independent support, after reaching a deal with Fianna Fáil before the weekend.

Mr Fitzmaurice said Independent TDs would be very focused on their talks: “it won’t be two hours here and there, we intend to do 12 hours a day until it is sorted,” he told RTÉ’s Morning Ireland.

Mr Fitzmaurice added he wanted to meet acting Minister for Health Leo Varadker with Ross and Mr Halligan to discuss cardiac services in Waterford.

Waterford TD Mr Halligan yesterday said unless he gets a deal on cardiac care for the southeast he will not back a Fine Gael minority government, and that he has the support of the other five Independent Alliance TDs.

However, some of his fellow Independents told The Irish Times that, while they would support Mr Halligan, they will not let a single issue derail an agreement bringing them into government.

Mr Fitzmaurice said: “We want a proper health service for the whole country not just Waterford. I will support John Halligan, but there is no whip system, we work together and won’t need to follow each other.

“The most important thing is a Programme for Government. We will sit down and analyse it, take it one step at a time.”

Another Independent TD, Mattie McGrath, said on Monday the ship of State had to move in another direction.

Speaking on Newstalk’s Breakfast programme Mr McGrath said he was keen to see the document that had been agreed between Fianna Fáil and Fine Gael.

Mr McGrath is hoping that mortgage arrears, interest relief, rent allowance along with rural and regional issues “from outside the Pale” will be included in the document. “We haven’t put local issues first” he added.

Mr McGrath said he knew how hard Mr Coveney had worked on the talks, but he felt it was “a bit presumptuous” to think it would all be agreed this week.

“There’s no point in buying a pig in a poke, there’s a lot of talking to be done yet. We want to see the facts and figures.”