"This whole set of (judicial) bills is a scandal", said Agnieszka Janczarska, a 39-year-old lawyer in Warsaw who attended both demonstrations.
Police estimated the crowd at 4,500 people, while the city authorities said there were more than 10,000 protesters at the demonstration, organised by the KOD pro-democracy movement, which is critical of the governing conservatives' policies on courts as well as other areas such as media and education.
Jaroslaw Kaczynski, Poland's most powerful politician and leader of the Law and Justice party, contends that the courts are rooted in the communist era and are working to protect those who served the previous system.
Activists brandished European Union and Polish national flags chanting "shame, shame" and "in defense of the courts" as they descended onto the streets of central Warsaw to rally against the draft bill.
Late on Friday the country's parliament, where the Law and Justice (PiS) party has a majority, passed a bill giving parliament a greater say in appointing judges, which critics say violates the constitutional separation of powers.
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Both texts were adopted earlier this week by the lower house of parliament and now they need only to be signed by President Andrzej Duda, who is closely allied with the PiS, to become law.
The judiciary has been a key locus of the political struggle in the first 20 months since PiS came to power. Critics of the changes argue the laws will erode the independence of judges and undermine Poland's democracy. The tribunal is the body charged with ruling on whether laws passed by the parliament are in accordance with the constitution. Current judges of the court could be retired under a PiS-backed bill.
Defending the new rules on the National Council, Deputy Justice Marcin Warchol said the change meant an "end to a corporation system, a system where the third power (the judiciary) was outside any control".
PiS supporters argue that the 1989 agreement that led to a gradual - and peaceful - end to communism in Poland didn't go far enough and in effect shielded ex-communists from prosecution after 1989.