Usage patterns
〈人〉が公務を行うto carry out official duties
The mayor carries out many official duties every day.
公務で〈場所〉へ行くto go somewhere on official business
The minister went abroad on official business.
公務に就くto take on public office/duties
He took on public duties at a young age.
公務を怠るto neglect one's official duties
The employee was disciplined for neglecting his official duties.