Environment Minister John Gormley has indicated that his party would support further cuts in December's Budget.
Finance Minister Brian Lenihan admitted yesterday that the €3bn to be slashed from public spending is a "minimum".
Speaking in Dublin this morning, Minister Gormley said nothing has been decided yet.
But he said the Green Party will support the Government in facing the challenges that lie ahead.
"We have met difficult challenges before and we are prepared to do so again," Minister Gormley said.
Meanwhile Tourism Minister Mary Hanafin has promised that the Government will be as sensitive as possible when deciding where to cut spending in the Budget.
Speaking today she said there is a huge amount of work still to be done on the Budget, and the Government is taking time to try and minimise the impact on families around the country.
"Last year we took €4bn out… and we took a long time looking at each of the different departments and then tried to balance (the cuts) out so that no individual family from a number of different angles.
"And we will do the very same again this year."