DUBLIN  Prime Minister Brian Cowen said late Monday that he would step down once a series of fiscal packages and budgets were in place next month, acceding to the demands of the opposition and its coalition partner, and injecting the threat of political instability into a financial crisis that already has markets on edge.

Earlier in the day, the minority Green Party declared that the public had lost faith in the government after its acceptance of a $100 billion rescue package over the weekend and that it would pull out of the government. It called for elections early next year, when a second round of austerity measures, forced on Ireland as a condition of the bailout, will be put before voters who have already suffered through three years of recession.

“The mood in the country is for an election and the people want a new mandate  that much is clear,” said Joan Burton, deputy leader for the Labour Party.

In agreeing to step down, Mr. Cowen became the first political casualty of the sovereign debt crisis in the 16-member euro zone. While Prime Minister George Papandreou in Greece has seen his popularity wane as the cuts mandated by the International Monetary Fund have begun to bite, he came out on top at a recent by-election and seems, for the moment, to have the backing of the country.