But Andersson said she had told the speaker of parliament she hoped to be appointed prime minister again as the head of a single-party government, and the prospects of that happening appeared fairly strong given support from other parties.
The Green Party quit after parliament rejected the coalition's budget bill.
"I have asked the speaker to be relieved of my duties as prime minister," Andersson told a news conference. "I am ready to be prime minister in a single-party, Social Democrat government."
The Green Party said it would support her in any new confirmation vote in parliament, while the Centre Party promised to abstain, which in practice amounts to the same as backing her candidacy. The Left Party has also said it would back her.
While these parties were unable to agree a budget, they are united in the goal of keeping the Sweden Democrats, a populist, anti-immigration party, from having a role in government.
"The Centre Party will open the door for her (Andersson) to be prime minister," its leader, Annie Loof, said on Twitter.
"We will make sure, again, that Sweden can have a government that is not dependent on the Sweden Democrats."
The opposition right-wing Moderates and Christian Democrats are backed by the Sweden Democrats, but cannot command a majority in parliament.