JAKARTA (Reuters) - The deputy chief of Indonesia's anti-graft agency will submit his resignation letter on Monday, days after the police named him a suspect in a false testimony case, an agency official said.

The police on Friday detained and questioned Mr Bambang Widjojanto, deputy chief of the Corruption Eradication Commission (KPK), for a case dating from 2010, fuelling tension between two law-enforcement bodies that have long had strained relations.

"Bambang will submit his resignation letter today," Mr Johan Budi, the KPK's deputy for corruption prevention, told Reuters.

Mr Widjojanto, who told domestic media on Saturday he was considering resigning, was not immediately available for comment.

KPK head Abraham Samad told domestic news website Detik.com on Saturday that he would not accept a resignation letter from Mr Widjojanto, who is one of four KPK commissioners.

KPK supporters believe Mr Widjojanto was named a police suspect in retaliation for the agency's decision to declare police general Budi Gunawan a bribery suspect on Jan 13. That announcement led President Joko Widodo to delay Mr Gunawan's appointment as the next police chief.

The police said its actions against Mr Widjojanto were not linked to the agency.

The apparent tit-for-tat actions reignite a rivalry between the graft-tainted police and the independent agency, popular among ordinary Indonesians for being a thorn in the side of the establishment.

Resolving the situation will prove an early test for Mr Joko, who took office in October pledging a clean government.