Poland also banned drone flights along its eastern borders with Belarus and Ukraine, and limited small air traffic there after shooting down what it said were Russian drones that violated its airspace on Wednesday.
Poland was backed by its NATO allies in shooting down the drones - the first time a member of the military alliance is known to have fired shots during Russia's war in Ukraine.
Russia said it had not intended to hit any targets in Poland, and it would make no further comment on the incident.
A senior NATO commander said it was not yet known whether the drone incursion was intentional.
But the incident has raised questions about NATO's preparedness against drone attacks, fuelled tensions with Russia and prompted some Western leaders to seek new sanctions against Moscow and question its commitment to peace efforts in Ukraine
"This Russian provocation, as the generals and our soldiers are well aware, was nothing more than an attempt to test our capabilities, our ability (in Poland) to respond," Polish President Karol Nawrocki told soldiers on Thursday.
"It was an attempt and provocation to respond, to test the mechanism of action within the North Atlantic alliance, our readiness to respond."
The Polish foreign ministry said the United Nations Security Council would meet at Warsaw's request, but did not say when.
The UN did not immediately comment, but Slovenia, Denmark, Greece, France and Britain have asked the Security Council to meet on Friday, diplomats said on Wednesday.
"(We are) drawing the world's attention to this unprecedented Russian drone attack on a member of the UN, EU, and NATO," Foreign Minister Radoslaw Sikorski said.
Polish F-16 fighter jets, Dutch F-35s, Italian AWACS surveillance planes and NATO midair refuelling aircraft scrambled in the operation to shoot down drones in Polish airspace overnight on Tuesday to Wednesday, officials said.
Polish Prime Minister Donald Tusk said on Wednesday it was "the closest we have been to open conflict since World War II", though he also said he had "no reason to believe we're on the brink of war".
Tusk called the incident a "large-scale provocation" and said he had activated Article 4 of NATO's treaty, under which alliance members can demand consultations with their allies.
US President Donald Trump spoke to Nawrocki on Wednesday, and the leaders expressed unity.
European leaders, who have been trying to persuade Trump to join them in tightening sanctions on Russia and boosting support for Kyiv, said the incident justified a collective response.
Neither Poland nor NATO has yet given a full account of what they suspect the drones were doing.
Air traffic restrictions imposed by Poland along the borders with Ukraine and Belarus are in effect and apply until December 9, and include limited small air traffic and a ban on civilian unmanned aircraft such as drones.
After visiting a military base, Nawrocki was due to convene Poland's national security council, which advises him on security threats.
"We will do everything to ensure that the allied commitments, which are so important from our point of view today, are fulfilled by our allies," Tusk told air force pilots at the base.
"So that we, as a country and you, as Polish pilots, are never alone, whether in times of peace or war."
