STORY: A handful of votes remain to be counted, but Andersson, who became Sweden's first woman prime minister last year, said the results showed the right bloc had won.
"In parliament, they have a one or two seat advantage," Andersson told a news conference. "It's a thin majority, but it is a majority."
Andersson said she would ask the speaker of parliament on Thursday (September 15) to relieve her of her duties as prime minister.
Ulf Kristersson, leader of the Moderate Party, is the right's candidate to be prime minister.
"I will start the work now with forming a new and vigorous government, a government for the whole of Sweden and for all its citizens," Kristersson said in an Instagram video post.
Andersson said she understood that many Swedes were worried a party with roots in the white-supremacist fringe was now the country's second biggest party.
"I see your concern, and I share it", she said.