Indonesia's popular anti-graft agency will be left "paralyzed" if police follow through with threats to name all its senior commissioners as suspects in various criminal cases, an agency official warned on Thursday.

The police last month named Bambang Widjojanto, deputy chief of the Corruption Eradication Commission (KPK), a suspect in a 2010 perjury case and are currently investigating complaints against the remaining three commissioners.

The move has ramped up tension between the two rival law enforcement agencies and prompted public outrage over what many consider a blow to anti-graft efforts in Southeast Asia's biggest economy.

Activists have rallied in support of the KPK, calling police actions a blow to the fledgling anti-graft movement in a country that consistently ranks among the most corrupt in the world, according to Transparency International.

"If the leaders of the KPK are named suspects one by one ... it is a fact that the KPK will be paralyzed," Johan Budi, deputy of chief of the agency's corruption prevention unit, told reporters.

If named a suspect in any case, an agency official is required by law to step down temporarily.

Widjojanto in late January offered to resign as deputy, but the agency's head has yet to approve the move.

Many believe the police are lashing out against the KPK after the agency last month named Budi Gunawan, a three-star police general who is President Joko Widodo's sole pick to be the next national police chief, a suspect in a bribery case.

Widodo has delayed Gunawan's appointment due to the controversy.

Police spokesman Ronny Sompie has said investigations into KPK officials are not linked to the anti-graft agency.

The KPK and police have a history of fragile relations. In 2012, police tried to arrest the KPK's lead investigator soon after it questioned the police inspector general over bribery allegations, but backed off after opposition from agency supporters.