The festivals will not require negative tests or vaccinations.
They wrote it was also signaling to others who speak out against mandates that their "voices will be silenced."
The police warning comes after the city declared a state of emergency on Sunday in response to the second week of protests.
The protests have fueled demonstrations in other countries against COVID-19 mandates, with authorities warning the U.S. could see similar disruptions soon.
Still, the developments have put the White House in an awkward position. The CDC continues to recommend mask use in areas of high and substantial transmission, which applies to most of the country.
The memo notes that the convoy plans to travel from California to Washington, D.C., and that drivers from Canada may join.
Quebec, which previously announced plans to punitively fine the unvaccinated, said Tuesday that most restrictions would be lifted by March 14.
"We want our freedom back," said another protester, identifying himself as Dave. "Jacinda (Ardern) has turned her back on us. Kiwis are not dumb. We are losing our jobs and our lives due to these mandates and restrictions."
In the city of Perpignan, near France's border with Spain, around 200 people gathered to set off towards Paris as part of the "freedom convoy" movement.