MANILA — A wave of violence has struck the central Philippine island of Negros, where at least 20 people have been killed in recent weeks in attacks that rights groups have tied to President Rodrigo Duterte’s efforts to suppress critics and opponents.

The latest attacks occurred on Saturday, when two people, a former town mayor and his cousin, were killed by unidentified gunmen. The local police said the killings were carried out by communist rebels, an assertion that the rebels and rights activists dispute.

The former mayor, Edcel Enardecido, 60, was a known supporter of the local wing of the New People’s Army, the armed unit of the underground Communist Party of the Philippines, which has broken off peace talks with Mr. Duterte’s government.

The police said that the two were ambushed by masked men who emerged from several vans in the town of Canlaon. Left-leaning groups have denied any connection to the killing of the two.