Nawrocki and his delegation had been travelling to Senegal, where he was scheduled to meet with the country's president and representatives of the African Union.
"At such a moment, the president must be in Poland. I am cutting short my flight to Senegal. I am returning," Nawrocki said on X amid a long-running dispute over the Constitutional Tribunal.
Police said officers entered the tribunal grounds following incidents outside the court, including objects being thrown at police.
Warsaw police later said officers were carrying out their statutory duties on the tribunal grounds but had not entered the building.
The deployment came after Constitutional Tribunal judge Anna Korwin-Piotrowska notified police of a possible threat to the safety of judges and tribunal employees and a risk of public disorder, state news agency PAP reported.
Police said they were also responding to requests from Justice Minister and Prosecutor-General Waldemar Żurek.
Meanwhile, a dispute erupted over the status of Constitutional Tribunal head Bogdan Święczkowski and his deputy Bartłomiej Sochański.
Public broadcaster TVP Info reported that Święczkowski had been suspended.
Żurek told reporters he had requested the lifting of the immunities of Święczkowski and Sochański for failing to fulfill their duties by preventing judges from performing their work.
The tribunal, however, said on X that Święczkowski remained its president and Sochański remained his deputy. It also described the actions against them as a "coup d'état."
Korwin-Piotrowska, the judge with the longest judicial service, told the media that she took over the tribunal's leadership and ordered a one-month suspension of the official duties of Święczkowski and Sochański.
Prime Minister Donald Tusk wrote on X: "Restoring the rule of law is our duty. After years of lawlessness under PiS, this process is difficult, at times even painful, and requires decisive action. There is no other way."
Chief Justice Zbigniew Kapiński, who heads the Supreme Court, condemned the government's actions, saying they were "unprecedented in a democratic state governed by the rule of law" and "raised serious questions" about their compatibility with Poland's constitutional order.
Kapiński particularly criticised the deployment of police to the tribunal grounds and the order suspending Święczkowski and Sochański.
He said police should not be used as a tool of political pressure on judicial institutions.
The dispute is part of a broader row over the rule of law and the judiciary between Tusk's centrist government and the right-wing opposition led by Jarosław Kaczyński and backed by Nawrocki.
Tusk said earlier this month that his government would use all available means to restore Poland's legal and constitutional order.
Nawrocki, an ally of Poland's former right-wing government, has failed to swear in three judges elected by parliament, while Święczkowski, a former deputy justice minister under that government, has refused to allow judges elected by the current parliamentary majority to take up their duties.
Tusk said the judges had been lawfully elected and accused the president of neglecting his constitutional duties.
The Constitutional Tribunal is responsible for ruling on whether laws comply with Poland's constitution.
Its legitimacy has been challenged in recent years because of disputed judicial appointments made under the previous government.
In December last year, the Court of Justice of the European Union ruled that the Constitutional Tribunal had violated fundamental principles of EU law and could not be considered independent or impartial.
The Luxembourg-based court said the tribunal had been compromised by "serious irregularities" in the appointment of three judges and its president, adding that those flaws undermined the rule of law.
Tusk said at the time that the ruling by the EU's top court gives his government the green light to "try to fix" the tribunal after years of legal turmoil under the previous administration.
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Source: IAR/PAP, TVP Info, Reuters