Mr Chumpol is accused of leading protesters to obstruct advance voting in Phasi Charoen district on Jan 26.
Mr Tarit said the Centre for the Administration of Peace and Order (CAPO) would take action in support of the court's arrest order.
He made the announcement after the first meeting of CAPO, since the emergency decree was replaced by the Internal Security Act (ISA).
CAPO has been reinstated to replace the Centre for Maintaining Peace and Order (CMPO) now the decree has been lifted.
Despite the change, caretaker Labour Minister Chalerm Yubamrung will continue to act as director of the organisation, he said.
"CAPO, with support from the police, military and civilian personnel, will do its best to perform its duty according to the law to restore peace and order in the country," Mr Tarit said.
He added that the lifting of the emergency decree has no bearing on legal action being taken against PDRC leaders who committed legal offences in connection with anti-government protests.