Minister for Agriculture Simon Coveney has said the size of the No vote and the low turnout for the Children's Referendum will not affect the Government's attitude to change the Constitution when and where necessary.
Asked whether Sunday's result would mean other planned referendums would be delayed, the Fine Gael TD said it would not.
The referendum was passed, though not by as wide a margin as had been expected with 58% voting Yes and 42% voting No.
Turnout was low at 33.53%, the lowest since the 1996 referendum on bail.
Mr Coveney said he expects the Government to hold more referendums before the end of its term.
He added that he has absolute confidence in the Attorney General following last week's Supreme Court decision against the Government's information campaign for the Children's Referendum.
He said the Cabinet will listen to what Máire Whelan has to say at today's meeting and make decisions off the back of that.
Minister for Education and Skills Ruairi Quinn also said he has every confidence in the Attorney General.