She has called the government's move "a purge of the Supreme Court conducted under the guise of retirement reform".
Chief Justice Malgorzata Gersdorf has refused to stand down from her post.
So what's next in the stand-off?
According to Amnesty International, judges in Poland are "experiencing political pressure" in connection with the PiS judicial reforms that critics insist pose a threat to the separation of powers that is key to democracy.
Gersdorf, who has been the president of the Supreme Court since 2014, believes the legislation is unconstitutional and can not be implemented. It forces the retirement of about 40 percent of the Supreme Court's justices - 27 out of 73.
"We contest the law, but we can not directly invoke the constitution, so we have complied with it", Michal Laskowski, a Supreme Court justice, told the liberal Gazeta Wyborcza daily.
If that goes ahead, the ruling party will effectively control the Supreme Court, he said, which as well as being the country's highest court of appeal has responsibility for ensuring the validity of elections.
Their supporters say the law was aimed at certain judges and had little to do with age, an argument that was bolstered when the government named Justice Gersdorf's replacement: the 66-year-old judge Jozef Iwulski.
Democracy champion and Nobel Peace Prize victor Lech Walesa has said he will come to Warsaw Wednesday to defend the Supreme Court.
Gersdorf was back at work again Thursday, firm in her position that the constitution sets her term as chief justice at six years, overriding the new law.
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Jaroslaw Kaczynski, the ruling party leader, said in an interview published Wednesday by the Gazeta Polska daily that the judges' "action" will result in their "shameful disaster".
The crowd chanted "Judges are not removable!" and "Constitution!" and then marched to the Presidential Palace to show their disapproval of the law co-authored by President Andrzej Duda.
Prime Minister of Poland Mateusz Morawiecki said this in his address to the European Parliament on Wednesday, an Ukrinform correspondent reported.
Further demonstrations are planned outside the court on Wednesday evening.
But the government says the changes will help fight corruption and improve the court's efficiency.
The government has refused to back down despite the European Union legal action, insisting the changes are needed to tackle corruption and overhaul the judicial system.
Manfred Weber, a German member of the conservative European People's Party group, hailed Poland's great democratic legacy, praising the 10 million Poles who joined Solidarity in the struggle against communism in the 1980s.
The European Commission, which polices compliance with EU laws, opened an infringement procedure Monday against Poland over the Supreme Court law.
Pro-democracy protesters who massed outside the court on Tuesday waving European Union and Polish flags said they would stage more rallies across the country on Wednesday.