"The situation ... has nothing in common with the real condition of our country," Prime Minister Szydlo said in a televised address.
"On the contrary, it reflects a sense of helplessness and frustration on the part of those who lost power and don't have nay ideas how to attract Poles to their views."
Earlier on Saturday, European Union Council President Donald Tusk, a former head of the PO - Poland's largest opposition party - urged the government to "respect and regard the people, constitutional principles and morals."
"Those who undermine the European model of democracy (and) attack the constitution and good customs, expose all of us to strategic risks. By throwing away the spirit of freedom and community, they write the next act of Poland's solitude," Tusk, who has a long-standing feud with PiS head Jaroslaw Kaczynski, told a conference in Wroclaw.
At Saturday's protests in a freezing Warsaw, opposition leaders served hot tea to the police and some of the 5,000 demonstrators who held banners saying "Free media" and carried Polish and European Union flags.
"If it becomes clear that it is impossible to talk to (PiS lawmakers), we should have early elections," Ryszard Petru, head of the liberal Nowoczesna grouping, told the protesters.
A snap election is unlikely, however, as PiS has a majority in parliament and could block any vote of no confidence.
One EU diplomat said the protests highlighted divisions in Poland but did not represent a growing anti-government movement.
"The people who have gone out to the streets are essentially those who are anti-government from the beginning," said the diplomat.
"I am not getting a feeling that people are ready to go up and protest. It doesn't mean they won't one day,"