Speaking before a Cabinet meeting on Tuesday, Tusk said that, according to all available data, the drone had entered Lithuania "from the Polish side."
He said he would discuss the incident with Lithuanian President Gitanas Nauseda later in the day and promised that all circumstances would be examined.
Tusk added he expected "full cooperation" from Ukraine.
He would act "without emotion, without any ill intent," he said, but would be "very insistent" in seeking answers.
Poland’s operational commander will formally request an explanation.
"Regardless of the outcome, Poland does not permit operations on or over its territory without the explicit consent of the Polish state," Tusk said.
"That will not change, regardless of who would carry them out."
Lithuania’s defence ministry said debris of a drone that violated its airspace was found in the north of the country.
The aircraft exploded and damaged a civilian vehicle. No casualties were reported.
Lithuanian Prime Minister Mindaugas Sinkevičius said on Monday that Ukraine had confirmed losing contact with one of its drones on Sunday.
He added that it was an FPV drone carrying explosives and that it had flown into Lithuania from Poland.
Polish Defence Minister Wladyslaw Kosiniak-Kamysz also said the latest findings pointed to a Ukrainian drone.
The incident came as Ukraine launched a drone attack on St Petersburg and surrounding areas overnight into Sunday, hitting targets including an oil terminal, a data centre of the VK social network and a logistics hub of retailer Ozon.
Local authorities said 144 drones were shot down over the Leningrad region.
Air raid alerts were sounded in Lithuania and Latvia at the same time.
On Tuesday, Sinkevičius said Lithuania would begin consultations with NATO on changing procedures to allow objects violating its airspace to be shot down without first being visually identified.
(ał/gs)
Source: PAP