By NEKTARIA STAMOULI, The Wall Street Journal

Greece's government moved quickly on Wednesday to quell rising concerns over politically motivated violence after a self-professed member of the country's far-right Golden Dawn party was implicated in the overnight killing of a prominent left-wing artist.

A 34-year-old rapper known for his anti-fascist views, Pavlos Fyssas, was stabbed to death early Wednesday in a working-class neighborhood near the port of Athens. Police said they have arrested a 45-year-old man, and said that he has confessed to the killing and told them he belongs to Golden Dawn.

Police said late Wednesday that he had not been charged yet and no court date was set.

Following the killing, police searched party offices to investigate any links with the suspect. The party has denied any connection to the killing.

Greece's Public Order Minister Nikos Dendias said the government would amend the country's criminal code with the aim of making it easier to prosecute political attacks.

"Neither the state will tolerate, nor society will accept, acts and practices that undermine the legal system," Mr. Dendias said.

The killing of Mr. Fyssas comes after a series of violent attacks in recent days allegedly by members of the party against political rivals, including both communist activists and a center-right mayor in southern Greece.

Extremist tactics have characterized the Golden Dawn party in the past. It has focused mainly on immigrants but, on occasion, followers of the group have also clashed with left-wing anarchists, among others.

Golden Dawn says it condemns acts of violence against others.

After six years of recession and 3½ years of harsh austerity measures, Greece has seen a radicalization of its political landscape.

The far-right Golden Dawn party—which many here identify as neo-Nazi based on its logo and rhetoric, an identification the party rejects—has raised eyebrows by proposing that Greece's borders be mined to stem an influx of illegal immigration.

It first entered the Greek Parliament during the last elections in mid-June 2012 and its popularity has risen since then. Recent public-opinion polls show it is the third-most-popular political party with 10%-12% of the vote, trailing only the governing New Democracy party and the left-wing opposition Syriza party.

Center-right New Democracy, which dominates the country's two-party coalition government, has been criticized for soft-pedaling the threat posed by Golden Dawn in an effort to lure back some of its traditional voters who have drifted to the far-right party. New Democracy has dismissed the criticism, saying it was the first to condemn the recent acts of violence.

Police say about 5,000 people demonstrated in the afternoon at the site of the killing. Sporadic violence broke out later, as self-styled anarchists hurled rocks and Molotov cocktails at the police, who responded using teargas.

The right-wing politician Panos Kammenos, who heads the Independent Greeks party, was also attacked by some in the crowd as he arrived to honor the victim and had to leave.

Political parties from across the spectrum condemned the killing. President Karolos Papoulias decried the political violence as a "repulsive phenomenon."

Government spokesman Simos Kedikoglou appealed for a common front against political extremism.

"We are asking for all the political forces to raise a rampart against the vicious cycle of conflict and violence," Mr. Kedikoglou said. "Democracy requires stability, judgment and responsibility from everyone."

This past weekend, Golden Dawn members disrupted two events commemorating Greece's occupation during World War II. In a ceremony in the northern town of Giannitsa—honoring townspeople killed during the German occupation—a Golden Dawn member enacted a Nazi-style Sieg Heil salute after laying a wreath at the town's memorial. In a separate event in the southern Peloponnese, two Golden Dawn members of Parliament led a small group of protesters who disrupted the ceremony and seized the microphone from the local mayor as he was giving a speech.

Earlier this week, a Golden Dawn deputy described Muslim deputies in the Greek legislature as traitors and agents of rival Turkey.

Last Friday, police said some two dozen Golden Dawn members were detained in a police raid after being linked to a violent attack against Communist Party members in another working-class district near the port of Athens, not far from where Mr. Fyssas was killed.

Nine Communist Party activists were taken to the hospital with serious injuries after being savagely beaten as they were putting up posters on the street. Golden Dawn has denied any connection with the attack.