Plans are also underway to allow the justice minister to get rid of all of the country's Supreme Court judges and appoint new ones, adding to global concerns about Poland's democratic credentials.
Chanting "we will defend democracy" and waving European Union and Polish flags, around 4,500 protesters attended demonstrations in the Polish capital, according to police.
A Polish opposition party said Saturday it had urged leaders of worldwide organizations to send observers to parliament to oversee voting on a law that would force the entire Supreme Court into retirement and impose ministerial control over the selection of judges.
Kaczynski, a lawyer, contended that the judiciary sector has not been reformed since communist times, lacks moral principles, is inefficient and needs younger personnel.
The opposition and some European politicians say these moves snuffed out judicial independence and violated democracy and the rule of law.
The bill must now be signed by the president to become law, but a protest against the change was scheduled to take place in the capital Warsaw on Sunday.
Critics have accused PiS of dismantling the rule of law in Poland and of aiming to stack courts with its own candidates.
"Today we know that a great fight has begun and we know we must be together, we know we must fight against them together", Grzegorz Schetyna, leader of the largest political grouping, the Civic Platform, told the crowd during the rally.
Poland's TVP television, controlled by the state, said the protests and calls to block Tuesday's debate were "an attempt to organise a coup against a democratically elected power".
Police estimated the crowd at about 4,500, a number far lower than city hall estimates, which put the number above 10,000.
In the evening several thousand people gathered in front of the Supreme Court building next to Warsaw's historic centre, holding candles in a peaceful protest "in defence of courts and democracy".