Green Party Leader John Gormley has said a meeting of his party's TDs, senators and councillors had been open, frank and productive.
Mr Gormley told a news conference that major concern was expressed about the implications of cutbacks in the education area but that people had been committed to the continuing participation of the Green Party in government.
He said education spokesman Paul Gogarty would be meeting Minister Batt O'Keefe to discuss ideas on how savings could be made that would not impact on school children.
As Green Party public representatives met in Dublin to discuss the Budget, a Green councillor has said she would be advocating that the party vote at its conference next year on whether it should remain in Government.
Dublin North Central representative Bronwyn Maher said it looked like the party was selling out on its core policies.
Earlier, Mr Gogarty confirmed his party would be supporting the Government during this week's Dáil debate on education cutbacks.
On RTÉ Radio's News At One, he said the Greens would try to see if a solution could be found within the budgetary parameters.
He said that the education partners would have a valuable role to play in identifying how savings could be made.
Tánaiste Mary Coughlan has said there will be no changes to the budget proposals on education.
Speaking in Dublin, she said she had no concerns that the Green Party was not supportive of the Budget and that she was confident it would remain part of the Government.
Some within the Green Party have expressed concern about the proposed cutbacks in education, which will be at the centre of a Dáil debate tomorrow and on Thursday.
Fianna Fáil and Taoiseach Brian Cowen need the Greens' support in Thursday's vote on the Labour motion.
Mr Gogarty had already called for the cutbacks to be reversed and had suggested alternatives to Mr O'Keeffe.
Mr Gormley has said the Greens were in Government for the long-haul but councillors worried about their prospects in next year's elections may have a different view.
They have already voiced their opposition to the medical card cuts and will be just as unhappy about many other Budget provisions.
Earlier, Mr O'Keeffe ruled out any row back on the proposed cuts in education.
Speaking to RTÉ this morning at University College Cork, the Minister said what he was now proposing in regard to class sizes was one step back to take two steps forward.
He added that what he was now doing in education will not affect the education system in the long term.
He said one of reasons for the success of the Celtic Tiger was the marvellous education system in this country and that class sizes were bigger then.
Regarding third level fees, he said he has four more months to report back to the Cabinet about funding but that he did not rule out introducing either fees or loans in the future, adding those who can afford to pay fees should.
IPPN urges Govt to rethink
The Irish Primary Principals' Network has called on the Government to reconsider planned cuts in spending in education.
The network has a membership of 5,100 principals and deputy principals representing 90% of all primary schools.
It says upwards of 1,000 teachers would be lost to the system as a result.
Network Director Sean Cottrell said it was unthinkable that consideration would be given to cutting back on an educational infrastructure that has served the country so well.
'Recent history shows us that our education system is an essential part of the Ireland's infrastructure.
'Just as it is unthinkable that we would dismantle our transport infrastructure in the face of economic pressures, so too is it unthinkable that we would consider cutting back on the educational infrastructure which has served, and continues to serve us so well,' he said.
