After President Olafur Ragnar Grimsson formally asked Ms. Sigurdardottir to lead a new government, she signaled at a news conference that she planned a shake-up of the Haarde government’s policies, particularly on housing and jobs. “All the ministers in my cabinet must work fast, take firm action and accept responsibility for their actions,” she said. “The people of this country must see that there is a new government in place which will defend their homes and rebuild the job market.”

Ms. Sigurdardottir comes to the prime minister’s job with a formidable reputation. As social affairs minister in several governments since 1987, she is credited with pushing through policies that widened housing opportunities for Iceland’s poor and strengthened the social welfare system. She has said she will use her powers as prime minister to push for debt relief for the most vulnerable Icelanders.

She began her political career as a union organizer with the national airline, now known as Icelandair, where she had worked more than 30 years ago as a flight attendant. She has two sons with her former husband, a banker, and six grandchildren. Ms. Sigurdardottir established a civil partnership in 2002 with Jonina Leosdottir, 54, an author, playwright and journalist. She, too, is a divorced mother.

Although Ms. Sigurdardottir’s rise has drawn widespread attention on Web sites for gay men and lesbians outside Iceland, her relationship is considered unremarkable at home. In 1940, while still a dependency of Denmark, Iceland decriminalized gay sex. It approved civil partnerships for gay and lesbian couples in 1996, one of the first countries to do so.

“Iceland is a small society, and the public knows what Sigurdardottir stands for as a politician, and that’s the only thing that is important,” said Frosti Jonsson, a spokesman for Iceland’s National Association of Queers. “Nowadays, not only does Iceland have one of the most progressive legal environments for gay people, there have also been changes in public attitudes towards gay people. It simply isn’t an issue anymore.”