Members of the Independent Alliance and new Fine Gael leader Leo Varadkar have held what both sides called a "constructive" meeting tonight.

In a statement, the Independent Alliance said they "stressed the need to accelerate various pieces of recent legislation as negotiated in the Programme for Government".

The grouping said Brexit, rural affairs and infrastructure were discussed, among other issues.

A statement from a Fine Gael spokesperson said the wide-ranging discussions "focused on how to make further progress on commitments in the Programme for a Partnership Government", as well as where free votes will apply.

Ahead of the meeting, members of the Independent Alliance said they would seek further free votes on issues that are not in the Programme for Government and which are also not covered by their Cabinet responsibilities.

Shane Ross said they had found it a sore point over the last year and they had difficulties with issues of conscience.

The alliance is to hold a second meeting with Mr Varadkar later this week, once the Fine Gael leader has raised the issues with particular line ministers.

Noting earlier that Mr Varadkar had proposed merging the USC with PRSI during the Fine Gael leadership contest, ministers of State Kevin Boxer Moran and John Halligan both said they were sticking by the Programme for Government pledge to phase out the USC.

They also stated that they wanted certain legislation introduced and passed in the Dáil by the summer recess.

Discussions between Mr Varadkar and the other Independents supporting the Government including Minister for Communications Denis Naughten, Minister for Children Katherine Zappone and TD Michael Harty are planned for tomorrow.

Dr Harty said he will enter the "conversation" with an open mind.

Meanwhile, a spokesperson has said Mr Varadkar is not aware of any "understanding" between the Government and Independent TD Michael Lowry.

The Tipperary TD has consistently voted with the Government since it was formed over a year ago.

Mr Lowry has told RTÉ News that he has not yet decided how he would vote when Mr Varadkar is nominated in the Dáil next Tuesday.

He said he would consult with his constituency team and make a decision before the end of the week.

But he wants to see a "consolidation" of the "understanding" he has with the Government, he said.

Fianna Fáil leader Micheál Martin will meet Mr Varadkar tomorrow.

Mr Martin has already said he wants the Government to make more progress in tackling the housing crisis and to improve access to health services.

He also wants discussions around the next budget to be "open, transparent and with no surprises".