The biggest demonstration took place in the capital Warsaw where around 20,000 protesters gathered outside the public television headquarters, according to city hall estimates.
The protesters waved Polish and European flags, shouting "Free media, free Poland" as well as anti-government slogans.
The demonstrations organised by a citizens' initiative, the Committee for the Defence of Democracy (KOD), were held in around 20 cities mainly outside the regional offices of the TVP public television network.
Polish President Andrzej Duda on Thursday had signed the controversial bill into law which allows the treasury minister to appoint -- and sack -- senior figures in public radio and television, who will no longer be hired through contests organised by the National Broadcasting Council
Critics see the move as the latest bid by the ruling Law and Justice (PiS) to consolidate power and render ineffective any organ that could keep it in check since taking power late last year after eight years in the opposition.
The PiS said earlier it planned to turn the PAP news agency and public television and radio -- all currently state-owned businesses -- into national cultural institutions like the opera or the national museum.
Several international press organisations criticised the law as did the Council of Europe, the continent's top human rights watchdog.
French Culture Minister Fleur Pellerin said Poland's new media legislation "profoundly goes against" Europe's "underlying values".
In an unprecedented move, the European Commission is set to debate the state of rule of law in Poland on January 13, which could lead to potentially punitive measures.
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