The government wants to change the way the court works, but the court says the changes are unconstitutional.
The government has refused to publish the court's ruling because to do so would make it binding.
Critics say the changes would limit the court's ability to scrutinise government legislation.
Since it came to power last October, the new government of the conservative, populist Law and Justice party (PiS) has regularly clashed with the media and the opposition.
In Warsaw, demonstrators waving Polish and EU flags marched from the Constitutional Court to the presidential palace. Rallies also took place in the cities of Poznan and Wroclaw.
The government says the protests are proof that democracy is thriving in Poland. It argues that it won a strong mandate in elections last October to introduce sweeping reforms.
Why is Poland worrying the EU?
Government takes control of state media
The new rules increase the number of Constitutional Court judges needed for a ruling and change the order in which cases are heard.
Last week, the Constitutional Court struck down the rules as unconstitutional.
The Polish government has refused to publish the court's decision, saying the judges were not following the very rules they were evaluating.
The new rules will now go to parliament for debate, a government spokesman told a news conference on Saturday.
Last month, a draft report by the Council of Europe - a human rights watchdog - said the changes made it extremely difficult for the court to take decisions, thereby endangering the rule of law.
Thousands of people are protesting in the Polish capital Warsaw as a constitutional crisis between the government and the top court deepens.