Metro Manila (CNN Philippines) — Senator Ping Lacson and Ifugao Representative Teddy Baguilat want the Senate and the House to investigate the killing of Albuera, Leyte Mayor Rolando Espinosa due to a shootout inside a jail cell on Saturday.

Lacson said in a statement he believes the mayor's death falls under extrajudicial killing and is a possible cover-up for certain personalities.

The senator said he cannot wrap his head around the questionable circumstance of Espinosa's death. He asked how a prisoner detained in a cell could think of fighting back against police officers serving his warrant of arrest.

Looking to the authorities, Lacson asked why Criminal Investigation and Detection Group (CIDG) officers went to search the jail cells and not ask a sheriff to serve the warrant since they were already detained. He also questioned why there was a need to serve the warrant if the CIDG operatives could have simply coordinated with the jail warden.

He asked why inmate Raul Yap was also killed, "the only other prisoner inside the cell was also killed, therefore no witness could testify."

Related: Albuera Mayor Espinosa, 1 other inmate killed in jail cell shootout

Lacson dared the authorities to answer and prove the veracity of their narrative that Espinosa and Yap were the ones who first fired their guns, causing the police to retaliate — which led to the inmates' deaths.

"I think that incident is the biggest challenge to the credibility of the PNP (Philippine National Police) that could affect even the other operations involving drug suspects killed under similarly suspicious circumstances," he said.

Lacson said he will discuss the possibility of resuming the Senate's extrajudicial killings investigation, which will focus on the death of Espinosa and also the ambush killing of his lawyer last August.

'So many irregularities'

Rep. Baguilat criticized on Twitter the CIDG's narrative of the incident.

"PNP says the mayor was killed inside prison while fighting back with a gun as he was about to be served a warrant. Sino niloko nyo? (Who are you kidding?)," he tweeted on Saturday.

He said there are "so many irregularities in the story" that a warrant was served early in the morning to someone who was already detained.

Baguilat said he will call for a Congressional inquiry into the killing of Espinosa.

The Department of Interior and Local Government Secretary Ismael D. Sueno ordered the PNP to investigate the incident immediately. The Commission on Human Rights will also conduct an independent investigation.

CIDG 8 Regional Chief Marvin Marcos said they served search warrants against Espinosa for illegal possession of firearms and Yap for illegal drug transaction.

Marcos said a shootout ensued when Espinosa and Yap fired at the police.

Espinosa is one of the government officials linked by President Rodrigo Duterte to the illegal drug trade.

His son, Kerwin was arrested in Abu Dhabi on October 27. He is now under the custody of authorities in Abu Dhabi, and they are processing his return to Manila to face charges of drug trafficking.