Fine Gael has told Independent TDs no local deals will be offered in return for their support.
Five TDs met with the party for an hour and 40 minutes to discuss backing a minority Government.
Independent TD Mattie McGrath said there was no discussion about Cabinet seats or Ministerial portfolios.
He said agreements at a local level were ruled out.
Roscommon TD Denis Naughten said the issues were common across all constituencies.
He said they included jobs, health, rural decline, broadband and they existed in Donegal, Roscommon and Tipperary.
“We have seen the economy in Dublin expand and we have seen the turnaround of the recession here but we have not seen it outside of the M50 and all of us have common issues.
“That point was made quite clearly to us today. This is an issue for backbenchers in Government and for TDs on the opposition benches.”
Mr McGrath said the priority for all sides was to form a Programme for Government.
The five Independents insisted they have made no decision on who they would support for Taoiseach on April 6th.
Clare TD Michael Harty said the purpose of the meeting was to build trust and a relationship with the Fine Gael party.
He said this would be a new way of governing but stability was essential.
The five TDs were Mr McGrath, Mr Naughten, Mr Harty, Galway West TD Noel Grealish and West Cork Michael Collins.
Speaking in advance of the meeting, Mr McGrath said the current political vacuum was not healthy for the country.
“We’re going to be looking for a fair share of the cake for rural Ireland,” he told Newstalk Breakfast.
“Fine Gael is already in government, they have shown more interest in talking to us. Fine Gael has more numbers. They have been pretty gregarious in their attempt to talk to us. They have power they want to hold on to it. That’s a good enough incentive for them.”
However, Deputy McGrath said Independent TDs believed there was no way forward without the co- operation of the second biggest party, Fianna Fáil
“We haven’t indicated who we are going to support for the office of Taoiseach. But we do believe that no one party can govern on their own without the co operation of the other.
“It’s down to basic mathematics. We wouldn’t be much good to anybody if the whole thing collapsed within a few months or by the first budget.”
The Fine Gael parliamentary party has given its assent to Mr Kenny to continue negotiations with Independents and smaller parties in a bid to form a government.
On Tuesday, Mr Kenny told his TDs and senators that any negotiations with Fianna Fáil would effectively shut down Fine Gael’s current talks with other individuals and parties.
Fianna Fáil deputy Willie O’Dea said on Wednesday there has been no contact “of any shape, nature or description” by Fine Gael.
“Our door is open, but they haven’t made any overtures and I don’t think they will until after April 6th.”
The Fianna Fáil Limerick TD rejected a suggestion put to him on Newstalk that the party was “playing cute hoor party games”.
“We have been engaged in intensive negotiations with the independents. Up to now our emphasis has been on policy and the people we’ve been talking to are the same.
Acting Minister for Agriculture Simon Coveney gave an update to the Fine Gael parliamentary party on Tuesday about the talks he and other ministers have been holding with a view to forming a government, and said Fine Gael now wanted to enter “structured dialogue”.
The next phase will be a roundtable discussion on Thursday involving interested parties.
Mr Coveney told the meeting Green Party leader Eamon Ryan was nervous about engaging in such a process but believed he would eventually do so.