Poland yesterday said it was stepping up security at vaccination points following two arson incidents overnight in a single town and an attempt by anti-vaccine activists to break into another.

"These incidents are recurring unfortunately," Prime Minister Mateusz Morawiecki told reporters.

"They will all be severely punished in accordance with current regulations and we will also carry out activities aimed at increasing the security of all these centres," he said.

Police chief Jaroslaw Szymczyk said arsonists had set fire to a mobile vaccination centre and an office used by the local epidemiological agency in the town of Zamosc in eastern Poland.

There were no casualties from the fires.

He called the incidents "extremely shocking" and said there would be "around the clock" security at vaccination points.

"Unfortunately we are observing an escalation of extremely brutal and even thuggish behaviour in anti-vaccine circles," he said.

Last month, police were called to two incidents involving vaccine sceptics -- one at a vaccination point in Grodzisk Mazowiecki where activists scuffled with security guards and medics.

The government has been encouraging Poles to get vaccinated, but the rate of vaccinations has slowed down sharply and remains relatively low in southern and eastern regions of the country.