MANILA — The Philippine police said on Thursday that a mayor had ordered the killing of a congressman who was gunned down shortly before Christmas, and that one of the men he hired to carry out the assassination had been arrested.

The police said they would seek to arrest Carlwyn Baldo, mayor of the city of Daraga, whom they accused of arranging the Dec. 22 killing of Rodel Batocabe, a member of the Philippine House of Representatives and an ally of President Rodrigo Duterte.

Mr. Batocabe was leaving Congress and had announced his intention to run against Mr. Baldo in Daraga’s mayoral election in May. Orlando Diaz, a police officer who was guarding Mr. Batocabe, was shot and killed along with the congressman at a gift-giving ceremony for senior citizens in Daraga, a city of about 125,000 in Albay Province, southeast of Manila.

“From all indications, as revealed by suspects and witnesses and physical evidence that was gathered by the police, the group that killed Batocabe and Diaz is a private armed group employed by the mayor that is involved in contract killing as a gun-for-hire syndicate,” said the national police chief, Oscar Albayalde.