The new measures, spearheaded by the ruling Law and Justice Party (PiS), will empower Parliament and the justice minister to appoint judges to the Supreme Court.
Protesters gather during a candlelight rally to protest against judicial reforms in front of the Supreme Court in Warsaw, Poland, July 16, 2017.
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 worldwide concerns about Poland's democratic credentials.
'Poland will cease not only to be a liberal democracy but a democracy at all, ' says opposition party.
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.
PiS says the party has a democratic mandate to make the judiciary more efficient and accountable to the public.
Sunday's demonstrations were the latest in a string of anti-government protests since the conservative and populist Law and Justice Party took office in 2015.
The opposition Kukiz '15 grouping has proposed that judges on Poland's influential National Council of the Judiciary (KRS) should be chosen either directly by citizens or by a qualified majority in parliament.
In a letter to U.N. Secretary General António Guterres, European Commission President Jean-Claude Juncker and the heads of several European tribunals and human rights watchdogs, the Nowoczesna (Modern) party said passing of the law would mean that "Poland will cease not only to be a liberal democracy but a democracy at all".
In December Poland saw its biggest political stand-off in years when opposition leaders blocked the parliament's plenary hall podium ahead of a budget vote, after objecting to plans by PiS to curb media access to parliament.
The Supreme Court supervises and provides guidance to lower courts on complex cases and can rule in disputed cases.
Smaller protests took place also on Sunday in Krakow, Katowice and other Polish cities.