Police around the US are being warned to wear bulletproof vests and avoid making inflammatory posts on social media after a man ambushed two officers and shot them dead inside their patrol car in New York City.

The gunman, 28-year-old Ismaaiyl Brinsley, had threatened retaliation for the slayings of black men at the hands of white police.

Investigators are trying to determine if Brinsley had taken part in any protests over the deaths of Michael Brown and Eric Garner, who have died at the hands of police in recent months.