On Monday, Geir Haarde, the former prime minister, announced his resignation, saying he regretted that his ruling coalition could not continue.
Haarde's government, a coalition between his Independence party and the Social Democratic Alliance, had been under pressure since the global financial crisis hit Iceland in October.
On Friday, the prime minister had called early national elections for May 9, revealing that he would not seek a new term because of a malignant throat tumour.
In negotiations with the coalition over the weekend, the Social Democrats had demanded the post of prime minister.
Haarde said: "We couldn't accept the Social Democratic demand that they would
lead the government."
Ingibjorg Gisladottir, Iceland's foreign minister and leader of the Social Democrats, was a potential replacement for Haarde.
Gisladottir said a more powerful leadership was needed.
"The government's actions in the last weeks and months were not swift enough," she said.
On Sunday, Bjorgvin Sigurdsson, Iceland's minister of commerce, resigned over his part in causing the economic crisis.
Sigurdsson, a member of the Social Democratic Alliance, said: "I have decided to do this to take responsibility. I realised last night that for me, at least, there is no