In a joint statement dated Friday, signed by all eight, the judges said they should be allowed to start work immediately.
They accused the president of an "arbitrary attempt" to select Tribunal judges, after he invited only three of them to take their oath at the presidential palace.
In their view, the constitution gives the president no role in choosing members of the Tribunal.
They say the law requires the oath to be sworn "before" him, but gives him no active part in it.
The judges who were not invited to the palace say they repeatedly asked to swear in Nawrocki's presence and received no reply.
They took the oath in parliament instead, which they say was valid, and passed a notarised record to the president.
They also accuse the Tribunal’s head, Bogdan Święczkowski, of blocking them from hearing cases for more than seven months.
The dispute dates back to March, when parliament elected six judges.
Nawrocki invited two to the palace, and four others swore in parliament in April.
Święczkowski did not let them work, saying the ceremony could not count as an oath "before the president."
Two more judges were elected later.
One swore at the palace in July, the other, Maciej Berek, took the oath in parliament on Wednesday.
Nawrocki said that if Berek had not sworn before him, he was certainly not a Tribunal judge.
Prime Minister Donald Tusk stressed that the judges had been lawfully elected and that the president was "abdicating" his constitutional duties.
He said the government would restore legal order by "the means available to the state."
On Tuesday, the Venice Commission, the Council of Europe’s advisory body on constitutional law, recommended that an oath without the president’s physical presence be allowed if he refuses or delays receiving it.
The row is part of a wider conflict over the rule of law between Tusk’s centrist government and the previous right-wing administration.
(ał)
Source: PAP