BERLIN — An avowed neo-Nazi has admitted to the murder this month of a member of Chancellor Angela Merkel’s center-right party, Walter Lübcke, who had defended her decision to accept refugees into Germany.

The 45-year-old suspect, identified by officials only as Stephen E. because of German privacy laws, confessed on Tuesday, Peter Frank, the country’s federal prosecutor, said on Wednesday.

“He claims to have planned and carried out the murder of Mr. Lübcke alone,” Mr. Frank said. But he added that his office would continue to investigate the possibility that the suspect had had help.

“Likewise, our investigation will continue to focus on whether that act, or murder, is based on a terrorist organization or whether the accused is a member of a right-wing terrorist group,” Mr. Frank said.

Mr. Lübcke, 65, who was the director of the regional authority in Kassel in the state of Hesse, in the western part of Germany, was shot in the head on the terrace of his house on June 2. His adult son alerted emergency workers, who took him to the hospital, where he was pronounced dead.

Two weeks after the killing, the authorities announced a political motive in the killing, and the suspect — who has a violent past and a police record, including a short stint as a member of the neo-Nazi N.P.D. party — was arrested. He was detained after DNA found on the victim’s clothes was matched in a criminal database, the authorities said.

Investigators said the suspect had led a relatively quiet life with a wife and two children in recent years, and had been an active and vocal far-right commenter online. As a young man, he tried to detonate a homemade explosive at an asylum center, according to reports in the German news media.

Mr. Lübcke appeared to have attracted the ire of far-right groups for suggesting at a town-hall-style meeting in 2015 that those who did not share the values of Ms. Merkel when it came to accepting refugees were free to leave the country.

News reports suggested that the murder suspect, Stephen E., had attended the meeting, but Mr. Lübcke’s speech was filmed and it was widely shared on right-wing forums. The video was recently recirculated online.

Since the killing of Mr. Lübcke, other regional politicians have said they have received an increasing number of death threats.

The confession on Tuesday was made after the suspect had been held by the police for nine days. It was announced at a parliamentary committee hearing on the killing Wednesday morning, and confirmed by Mr. Frank, the attorney general, shortly thereafter.

Follow Christopher F. Schuetze on Twitter: @CFSchuetze.

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