Prosecutors have asked Nawrocki to propose a suitable time and place for questioning, Anna Adamiak, spokeswoman for the prosecutor-general, said on Thursday.
The president said he would cooperate.
"I am a citizen, like every other citizen of the Republic of Poland," Nawrocki told reporters.
"All decisions I make, I make personally," he added.
He said the questioning would "certainly take place," although no date has been set.
Nawrocki is being called as a witness and has not been accused of wrongdoing in the case.
The investigation concerns four judges elected in March by the lower house of Poland's parliament: Marcin Dziurda, Krystian Markiewicz, Anna Korwin-Piotrowska and Maciej Taborowski.
They were among six judges chosen by parliament to fill vacancies on the Constitutional Tribunal, Poland's highest court for reviewing whether legislation complies with the constitution.
On April 1, Nawrocki accepted the oaths of two of the six, Magdalena Bentkowska and Dariusz Szostek.
His office said the position of the remaining four required further examination because of alleged errors during their election by the lower house.
All six subsequently took oaths in parliament on April 9. Bentkowska and Szostek were admitted to the Constitutional Tribunal, but tribunal head Bogdan Święczkowski refused to allow the other four to hear cases.
Prosecutors opened their investigation on April 21 after Bentkowska and Szostek filed a complaint.
Investigators are examining the circumstances in which the four other judges were prevented from performing judicial duties.
Nawrocki said on Thursday that he would not change his decision to refuse to accept their oaths.
He argued that anyone seeking a seat on the Constitutional Tribunal should have exceptional legal knowledge and said the four judges should have known that they needed to meet the president before taking office.
Nawrocki said their decision to take an oath in parliament had created grounds to exclude them from the tribunal. He told reporters he had asked the Constitutional Tribunal to resolve a dispute over the respective powers of the president and parliament in the appointment process.
The president also criticized the investigation, accusing Justice Minister Waldemar Żurek and the government of pursuing too many prosecutorial proceedings involving him.
"This is not serious for the Polish state, but of course I will submit to questioning," Nawrocki said.
A seventh judge, Sławomir Patyra, was elected by the lower house in June and took his oath before Nawrocki on July 28.
Patyra immediately said he would refrain from taking part in tribunal proceedings until the four judges elected in March were allowed to hear cases.
(rt/gs)
Source: IAR/PAP