It seemed like a new era was dawning in Sweden on Wednesday when Magdalena Andersson, the leader of the Social Democratic Party, became the country's first female prime minister.

But her historic term lasted less than a day.

She resigned on Thursday, a day after a painful budget defeat in parliament. She had only just formed a two-party minority government with the Green Party. But after their budget was rejected in favor of one proposed by the opposition, which included the far-right Sweden Democrats party, the Green Party the quit the coalition out of frustration, leaving Ms. Andersson's center-left party without a partner.

"According to constitutional practice, a coalition government should resign if one party leaves the government," Ms. Andersson said in a statement shared on her Facebook page. "For me, it is about respect, but I also do not want to lead a government where there may be grounds to question its legitimacy." She added that she had met with the speaker and asked to be dismissed from the her new position.

Ms. Andersson's resignation plunged Sweden into political uncertainty. The country's political landscape was already frayed by fragile coalition governments, and a vote of no confidence in June against the former prime minister, Stefan Lofven. Ms. Andersson later succeeded Mr. Lofven as leader of the Social Democrats.

Sweden, at one point, accepted more refugees per capita than any other European nation. But its progressive image has gradually been eroded by far-right populist sentiment that has taken hold, led by the Sweden Democrats party. The political spectrum has shifted to the right with increasing anti-immigrant and anti-European voices.

Per Bolund, a Green Party spokesman, said his faction left the government in frustration because Parliament had approved a state budget negotiated by the opposition, which includeda right-wing extremist party — the Sweden Democrats.

Until a new government is elected, the current one will remain on in the interim. Ms. Andersson, who served as Sweden's finance minister since 2014, has said she is still ready to serve as prime minister, but only in a one-party government.