However, partial results show the party losing support for the first time since 2010, when it entered parliament.
Sweden has two main political blocs, consisting of four parties on the right and four parties on the left. This means that coalition and minority governments are relatively common.
On Sunday evening, Andersson urged his supporters to wait for the final results, but added that if the current results hold, “there will be a new government in Sweden.”
Her party, the Social Democrats, has been a major force in Swedish politics since the end of World War II.
But the SD, founded by Nazi sympathizers in the 1980s, was shunned for years until 2022, when it became the country’s second-largest party after campaigning to tackle violent crime and immigration.
After voting on Sunday, Andersson laid out the choice facing the Swedish public: “Should we have a government completely dominated by the Sweden Democrats, which has never happened before in Sweden? Or should we have a government led by me, which will guide Sweden into a new spirit of cooperation?”
Kristersson, for his part, said it was important that he and his alliance were able to continue their work.
“I think we have genuine enthusiasm that we can continue our important work,” he said after voting in his home municipality of Strangnas.
The election campaign was dominated by national security, gang crime and welfare spending.