Tobias Baudin, party secretary for the Social Democrats, told journalists on Wednesday that if the election result remains as indicated when the vote count is completed on Thursday, with 176 seats for the opposition and 173 for the Tidö parties backing the current government, Kristersson will have to offer his resignation.
"Firstly, he needs to ring Magdalena Andersson and concede defeat and secondly, he needs to hand in his resignation as the country's prime minister."
Baudin's counterpart in the ruling Moderate Party, Karin Enström, said the party did not intend to take action until the voting was completed.
If the Moderate Party leader resigns, then the Speaker of the Parliament, Anders Norlén, can immediately begin discussions with party leaders over forming the next government.
If he decides to stay in place, then he will have to be ousted in a vote when the new parliament returns on September 29th.
Baudin said that as Kristersson had campaigned in the election as the leader of a four-party coalition and that that coalition had failed to win a majority, he could not claim the right to remain in place based on other possible constellations of parties.
"If this is the election result, the people of Sweden have rejected his alternative and voted 'no' to it, he says. It is obvious that he is now instead trying to cling on."
In 2022, Andersson phoned up Kristersson as soon as overseas votes and late votes had been counted on Wednesday and conceded defeat.
Kristersson on election night said he was open to seeking support from other parties for a centre-right government, indicating he hopes to induce the Centre Party to drop its support for Magdalena Andersson and support him instead.
"We're not in a hurry. Right now it's hard to see how this will turn out, given all the red lines," Kristersson said of the opposition.
The Centre Party has pledged not to support a government that includes Left Party ministers and the Left Party has pledged not to support a government in which it doesn't have ministers.