Green Party's leader John Gormley said: "The past week has been a traumatic one for the Irish electorate. People feel misled and betrayed."
"We have now reached a point where the Irish people need political certainty to take them beyond the coming two months," he added.
He called on Cowen and his Party Fianna Fail to pass an emergency budget next month, and then dissolve parliament early next year.
The call was echoed by the two main opposition parties, Fine Gael and the Labor Party.
Fine Gael leader Enda Kenny said in a statement: "What is needed now is an immediate general election so that a new government, with a clear parliamentary majority, can prepare the four-year economic plan, complete negotiations with the EU and IMF, and frame a budget for 2011."
Labor leader Eamon Gilmore also said it was "essential that we have a new government elected as soon as possible."