A right-wing bloc that includes a nationalist anti-immigration party has won a narrow majority in Sweden’s parliament. It marks a major political shift in the Scandinavian country that has a decades-long history of welcoming refugees, but that is grappling with a crime wave linked with immigration.

The center-left prime minister, Magdalena Andersson, conceded defeat with 99.9 percent of the vote from the weekend elections counted. She said she would step down Thursday.

The leader of the populist Sweden Democrats, Jimmie Akesson, declared victory for the four-party bloc. He said his party would be “a constructive and driving force” in the work of rebuilding safety in Sweden. He said it was “time to put Sweden first.”

The bloc that includes the Sweden Democrats — the country’s second-largest party — won a thin majority in parliament, but that does not mean Mr. Akesson will be the next prime minister. The reason is that in Sweden, the prime minister must be nominated by the parliamentary speaker for a vote in parliament. In order to win this vote, a majority of lawmakers must either approve the new prime minister or abstain from voting.

The parliamentary speaker has limitations as well: If four candidates are nominated without any of them successfully making it through a parliamentary vote, it triggers a general election. For now, though, Ms. Andersson said that “the preliminary result is clear enough to draw a conclusion” that her center-left forces had lost power.

Ms. Andersson became Sweden’s first female prime minister last year and led the country in its historic bid to join NATO following Russia’s invasion of Ukraine.

While Ms. Andersson is personally popular, anxiety in Sweden has grown over high crime rates in segregated districts that are home to large numbers of immigrants who have failed to integrate into Swedish society. Some blamed her Social Democrats, who have been in power for eight years.

The leader of Sweden’s third largest party, the Moderates, Ulf Kristersson, who’s considered to be the leading figure in the right-wing bloc and a possible prime minister, thanked voters for their trust. “Now we will get Sweden in order,” he wrote on Facebook.

“The Moderates and the other parties on my side have received the mandate for the change that we asked for. I am now starting the work of forming a new, effective government,” Mr. Kristersson said.

The Sweden Democrats were long shunned by Swedes because the party was founded in the 1980s by neo-Nazis and other far-right extremists. In recent years it has moved into the mainstream by expelling extremists, and gained support with a tough stance on crime and immigration amid a rise in shootings and other gang violence.

Its transformation was led by 43-year-old Mr. Akesson, who in his speech Wednesday evening said it was time for a new chapter in Sweden.

“Now it will be enough with the failed Social Democratic policy that for eight years has continued to lead the country in the wrong direction,” he said. “It is time to start rebuilding security, welfare and cohesion. It is time to put Sweden first. The Sweden Democrats will be a constructive and driving force in this work.”

The tally gave the right-wing bloc 176 seats in the 349-parliament, the Riksdag, and Ms. Andersson’s center-left bloc 173 seats. A majority in Sweden requires 175 seats.

“The four right-wing parties appear to have received just under 50 percent of the votes in the election, and in the Riksdag, they have gained one or two mandates. A thin majority, but it is a majority,” Ms. Andersson said. “Tomorrow I will therefore request my dismissal as prime minister and the responsibility for the continued process will now pass to the parliament speaker and the Riksdag.”