Tusk told parliament that Russia was expected to intensify its attacks on Ukraine, including in areas near Poland's border.
He said Polish intelligence services assessed that Russia could also launch strikes on countries supporting Ukraine.
"The potential, possible strikes will be, in quotation marks, accidental," Tusk said, describing a possible Russian strategy aimed at paralysing or weakening NATO countries' willingness to invoke the alliance's collective defence provisions in response to an attack on a member.
"There is a real risk that drones or other types of missiles could enter the territory of one or several NATO countries on the eastern flank and even cause damage," he said.
"The official narrative will be that it was an accident and that there is no reason for anyone to think about a NATO response," he added.
Tusk said Russia's goal would be to weaken NATO's cohesion and persuade its members that Article 5, which commits the alliance to collective defence, was "more theoretical than practical."
He said such "accidental" strikes could be repeated.
Tusk said the most likely scenario for the coming months, through early spring, involved “serious events" and required Poland to be "mentally prepared" for difficult challenges.
He said late autumn and winter were expected to be the most critical period of the war so far, according to information available to the government.
Tusk also warned of the growing use by Russia of jet-powered drones that can travel at higher speeds and altitudes before descending toward their targets.
He said relatively few countries were prepared to counter them effectively and that improving defences against the new weapons was a task for governments and politicians.
The Ukrainian military intelligence service reported the first use of Russian jet-powered drones in January, with their numbers increasing in subsequent months.
Tusk, Zelensky to meet in Ukraine on Friday
Tusk said he would travel to Ukraine overnight from Thursday to Friday to meet with President Volodymyr Zelensky and discuss possible cooperation through an "anti-ballistic coalition," including the use of Ukrainian and other countries' capabilities.
He said he would also discuss the situation surrounding Ukraine's energy infrastructure.
Tusk said an energy truce between Russia and Ukraine had not materialised despite US President Donald Trump saying on Monday that the two countries had agreed to stop attacking energy infrastructure.
"Since then, there have been many attacks, including on energy infrastructure in Ukraine," Tusk said.
"We therefore have to assume that this will continue, which also has consequences for Poland because these attacks are increasingly targeting installations very close to our border crossings with Ukraine," he added.
He said Russia's objective was to destroy Ukraine's economy and logistics on as large a scale as possible.
He said Russia was expected to continue attacks at a high frequency and intensity against six major Ukrainian cities, including strikes on warehouses holding supplies needed for the country's defence and attacks on railway infrastructure.
Tusk said the government had received information indicating that Russia was also considering hybrid attacks involving drones and missiles against countries supporting Ukraine, including Poland.
He also said Russia was not prepared for serious talks on a ceasefire or peace without what would amount to Ukraine's capitulation, based on information received by the Polish government about US-Russian consultations.
Tusk did not disclose the specific Russian demands, but said they would be unacceptable to Ukraine and other independent states and would increase the direct threat to European countries bordering Ukraine, including Poland.
He said Russia appeared to have little interest in serious negotiations at least until the end of winter and was counting on winter conditions to create a critical situation for Ukraine by disrupting supplies and targeting road and rail crossings and border infrastructure.
Tusk also said Russian attacks were causing heavy Ukrainian casualties, citing information from Ukrainian partners that he said indicated monthly losses of about 27,000 killed and wounded.
He said the figures represented the highest levels of casualties in the war.
The Polish government will strengthen Border Guard posts and infrastructure near the Ukrainian border, Tusk said.
Of 28 planned Hesco bastion shelters, 23 have already been completed, he said. The shelters are intended to protect border-crossing personnel and people in nearby areas in the event of an attack or other incident on the Polish side.
Tusk said the shelters were being built at Dorohusk, Zosin, Budomierz, Korczowa, Medyka and Krościenko.
He also said air defence systems would be expanded at six border crossings.
Forces from the 16th Airfield Renovation Battalion are being held in reserve to repair runways or railway infrastructure damaged in an attack, he said.
Poland's military and engineers would be prepared to rapidly repair and restore road, rail and, if necessary, energy infrastructure, Tusk said.
The warning came as Russia launched another major attack on Ukraine near the Polish border on Thursday.
A Russian drone struck about 4 kilometres from the Polish border, prompting Poland to scramble fighter jets and issue air-raid alerts in its eastern Lubelskie and Podkarpackie provinces.
Polish authorities said there was no violation of Polish airspace, and the military later ended its operations.
Tusk also warned that Russia's strategy could include attempts to influence political developments in European countries as elections approach.
He urged Polish lawmakers not to promote messages that could serve Russian interests.
Tusk called for political unity on the security of Poland's borders, airspace and citizens, and urged all political forces not to question Poland's commitment to its NATO allies and Article 5.
"As a country on NATO’s eastern flank, Poland will particularly need allied solidarity," he said.
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Source: TVP Info, IAR/PAP