The AGSI decision was taken at a special meeting of the national executive in Dublin yesterday and General Secretary John Redmond says he does not think there would be any chance of re-entering the process.
He said the options at the talks were like being asked "if you want to be shot with a shotgun or a handgun".
"There was no opportunity for getting anything that was palatable at all," he said
The Department of Public Expenditure has reacted to the decision with "disappointment", but says the talks will continue and made it clear that any group which leaves the discussions gives up the opportunity to shape the outcome.
Mr Redmond has warned that his members would resist all attempts to cut pay and the AGSI would not be involved in any process that reduced this money.
The General Secretary stressed that premium payments were a recognition of the frontline nature and the 24/7 role played by gardai.
Cuts to premium and Sunday pay and allowances were unacceptable and they were pulling out of the talks on the extension of the Croke Park Agreement.
Mr Redmond insisted they would not take part in talks while pay and allowances were on the table.
"Our members are working in the middle of the night," he said. "On the Sundays, on Christmas Day, when most people in regular jobs are with their families and that's their wont, that's okay, that's great for them, but our people have to provide a policing service on a 24/7 basis.
"On that basis, they carry out those duties and they're rewarded through allowances to a great extent for carrying out those duties in the middle of the night and on those days.
"We won't see a situation where we're negotiating how deep the cuts are going to go in reducing that package for our members."