The President of Iceland has asked Social Democratic party leader Ingibjorg Gisladottir to try to form an interim administration.
It is reported that Social Affairs Minister Johanna Sigurdardottir will be named as interim Prime Minister.
If chosen Ms Sigurdardottir, 66, will become the first openly gay or lesbian person to become a head of government.
She has been an MP since 1978 and was recently voted the most popular politician in Iceland.
Yesterday the country’s Prime Minister stood down and the entire Cabinet resigned.
A general election has been called for May 9th.
The government was toppled by the financial crisis, which severely affected the Icelandic banking system.
The International Monetary Fund began a $2.1bn (£1.49bn) bailout programme in December to stop the nation of 320,000 people going bankrupt.
Norway, Denmark, Finland and Sweden are lending Iceland an additional $2.5bn.
Prime Minister Geil Haarde had hoped he and his Independence Party could continue in coalition with the Social Democrats.
Negotiations broke down yesterday and the coalition was dissolved.
Mr Haarde, whose party currently have 25 of the 63 seats in the Althing (the Icelandic parliament), has annouced he will not stand for re-election, citing health problems.
At present the Social Democrats have 18 seats, the Greens have nine, the Progressive party has seven and the Liberal party has four.
“I have decided to ask the leaders of the Social Democratic Alliance and the Left-Green party to engage in conversation about forming a new minority government backed by the Progressive Party,” President Olafur Ragnar Grimsson said earier today.
“Therefore, I give Ingibjorg Gisladottir the mandate to lead the talks.”
Ms Gisladottir, 54, the country’s foreign minister, has been critical of the Prime Minister’s response to the financial crisis.
A former Mayor of Reykjavík, she has led her party since 2005.
She had brain surgery last week.
“We have taken the baton — the government should be operational before the weekend,” she told reporters after the President’s statement.