The policemen were among at least 11 people slain in the state on Saturday, including four children, according to local officials.
Veracruz Gov. Miguel Angel Yunes issued a video calling the killers "beasts" and "cowards" and repeated his vow to crack down on organized crime in the troubled Gulf coast state.
"We are going to do everything, whatever it may be," he said. "Veracruz will not be hostage to these animals."
The killing of federal police commissioner Camilo Castagne in the city of Cardel came two days after he had appeared with Yunes at an anti-crime event that was prompted by the discovery of dismembered bodies in bags left outside the office of a security official.
Yunes took office late last year following turmoil over the resignation of former Gov. Javier Duarte, who vanished while facing corruption allegations. He was tracked down and arrested in Guatemala in April and faces extradition proceedings.
Mexican prosecutors accuse him of using front men and shell companies to amass properties acquired with money stolen from the state.