Speaking as both daily coronavirus infections and deaths hit a record, Mateusz Morawiecki told reporters: "I have an appeal to all the protesters - let this anger, let this aversion focus on me, on politicians.”
He added: “But don't let it affect those who may be affected in two weeks, because you protesters will come into contact with some elderly people, on a bus, at home, at a meeting, and this can lead to drastic results."
His appeal came after seven straight days of demonstrations around Poland against a ruling by the Constitutional Tribunal which in practice signals a near-total ban on abortion in the overwhelmingly Roman Catholic country.
The street demonstrations have been held in defiance of rules that ban large gatherings amid the COVID-19 epidemic.
Poland on Thursday reported a record 20,156 new coronavirus infections and a record 301 new deaths, its worst daily toll since the start of the pandemic.
Morawiecki added that the number of hospital beds for COVID-19 patients in Poland was expected to rise to 31,000 or 32,000 by the end of next week, up from around 10,000 at the beginning of October and 23,000 at present.
He was speaking at the National Stadium in Warsaw, where a temporary hospital is being set up to treat people with the coronavirus.