A Chicago judge has banned a police union president from making public statements on the city's Covid-19 policy as a stand-off over vaccine mandates sparks duelling lawsuits, reports AP.

The dispute between mayor Lori Lightfoot and police union head John Catanzara has made the city the latest flashpoint in a deeply polarised debate over vaccines and whether governments have the right to mandate them.

Lightfoot sought and received an injunction against Catanzara when the judge issued a 10-day restraining order that bans him from making statements that encourage members not to report their vaccination status.

The police union filed its own lawsuit against Lightfoot and Chicago Police Superintendent David Brown that seeks to force arbitration over the matter.