Tusk told reporters before a cabinet meeting that he was told shortly after midnight that people with torches had been seen near the Russian border.
Forces were quickly sent to the area and a provocation had been prevented, "if that was the intention," he said, although this could not be fully confirmed.
He warned that tensions and escalation from Russia could continue and that Poland must remain on alert.
Tusk said allied intelligence services had been warning for some time of possible sabotage or more serious provocations, either on the Russian border or elsewhere in Poland.
General Alexus Grynkewich, who commands NATO and US forces in Europe, gave a similar warning during a visit to Warsaw this autumn, the Polish PM added.
After receiving information that armed people could enter Poland's territory in the first half of November, the government sent police to the north-east and reinforced the Border Guard and counter-terrorism units.
The operation is focused on the border with Kaliningrad, a Russian exclave between Poland and Lithuania.
A special headquarters in Warsaw is coordinating police, the army, border guards and intelligence services in the regions of Warmia-Masuria and Podlaskie.
Police chief Marek Boroń told private broadcaster RMF FM on Monday that the measures were preventive and aimed at protecting residents and local facilities.
Police have been ordered to stay on full alert from 2 to 8 November.
They denied claims in the media that the alert was linked to the Constitutional Tribunal, saying it was prompted by the threat of sabotage.
The news site Wirtualna Polska, citing its sources, reported that GROM special forces had also been sent to the north-east.
The military said they were there for training with police and other troops, and asked the public not to share photos or videos of soldiers or equipment.
Elsewhere in the region, Latvia’s interior minister said last month that armed, masked men escorting about 20 migrants from Belarus had threatened Latvian soldiers.
(ał)
Source: PAP, wp.pl, interia.pl, dkws.wp.mil.pl