The new measures will include efforts to prevent congestion and the buildup of vehicles, such as fuel trucks, at border crossings, Tusk said at an emergency meeting on Sunday.
Details are expected to be worked out in talks with the finance ministry on Monday, he added.
Tomasz Siemoniak, the minister in charge of Poland's security services, said they had assessed the situation at the meeting called by Tusk at the Government Centre for Security (RCB).
"Russia is attacking the Ukrainian economy and escalating tensions with countries supporting Ukraine," Siemoniak said.
"The Polish military, intelligence services and Interior Ministry are fully prepared and working to ensure Poland's security," he added. "Our services are also in constant contact with allied services."
During Russian attacks on Ukraine overnight into Sunday, Poland scrambled fighter jets and issued warnings to residents of border regions.
'We do not confirm such incidents'
Ukrainian authorities reported that a Russian drone struck a Kyiv-Warsaw train before it reached the Polish border and another hit near the Dorohusk-Yahodyn border crossing.
Tusk stressed the importance of verifying information and said Polish authorities had confirmed that a gas station or an area near one had been hit about 2 kilometres from the Polish border crossing, as well as a freight train standing on a siding.
He said reports that a convoy of trucks or a locomotive from the Kyiv-Warsaw passenger train had been attacked had not been confirmed by Polish authorities.
"I cannot say that they are untrue, but we do not confirm such incidents," Tusk said.
He also rejected speculation that Polish airspace had been breached.
"We also do not confirm speculation that something flew in from the Ukrainian side, meaning Russian in this sense," Tusk said. "Nothing violated Polish airspace that night."
Polish state railway operator PKP Intercity said 206 people had been travelling on the train from Kyiv and that none of the passengers were Polish citizens. The train was about 370 minutes late when it was handed over by Ukrainian railways, it said.
Tusk said the attacks near the Polish border showed that Russia was escalating its actions and using increasingly dangerous equipment, including jet-powered drones.
He said attempts to disrupt or paralyse border crossings were not new, citing similar incidents in Moldova. Russia's plans could include disrupting, paralysing or even destroying Ukrainian border crossings, he said, adding that this would also affect Poland.
Tusk warned that Poland could see "intensified actions" by Russia in the coming weeks and months and that an escalation could potentially extend to Polish territory.
He said he hoped "the worst-case scenario will not come true," but added that developments so far showed that "more serious scenarios are possible."
Polish Prime Minister Donald Tusk. Photo: PAP/Piotr Nowak
Early on Sunday, the Polish military said it had begun air operations in response to Russian attacks on Ukraine. F-16 fighter jets, helicopters and a SAAB airborne reconnaissance aircraft patrolled Polish airspace for several hours.
The Operational Command of Poland's Armed Forces said around 10 a.m. that the operation had ended and that there had been no violation of Polish airspace.
Defence Minister Władysław Kosiniak-Kamysz said Polish systems had detected an attack involving several Geran-5 jet-powered drones in western Ukraine. One struck about 1 kilometre from the Polish border and another about 5 kilometres away, he said.
During the operation, the Government Centre for Security sent alerts to residents of the southeastern Podkarpackie and eastern Lubelskie regions. A separate alert warned residents of six districts in Lubelskie province of the threat of an air attack.
Residents of the Włodawa, Łęczna, Świdnik, Krasnystaw and Chełm districts, as well as the city of Chełm, were told to seek a safe place, follow instructions from local authorities and await further information. Warning sirens sounded in the areas.
The air-attack warning was cancelled around 5 a.m., while an alert concerning the attacks in Ukraine was lifted around 9 a.m., Polish state news agency PAP reported.
Local authorities received reports of possible explosions, but no threat was confirmed.
Jacek Goryszewski, a spokesman for the military's Operational Command, said the reported bangs were believed to have been caused by fighter jets breaking the sound barrier.
He said the military issues alerts about air operations partly because such operations can result in increased noise.
Asked how close the potential threat had been to the Polish border, Goryszewski said some drones had operated and struck targets "very close to the border—several or a dozen or so kilometres from our borders."
He described the threat at the time as "real and close."
The Border Guard agency said border checks at Polish-Ukrainian crossings had been suspended overnight because of the Russian attacks. Traffic had returned to normal at all crossings by late morning.
Foreign Minister Radosław Sikorski, speaking on Sunday in Kyiv alongside Ukrainian Foreign Minister Andrii Sybiha, said attacks "just hundreds of metres from the Polish border" directly affected the security of Poles.
He said the attacks should be "final proof" that the security of Poland and Ukraine are inseparably linked and that solidarity with Ukraine and Ukrainians living in or seeking to enter Poland contributes to solidarity between the two nations.
Sikorski said Russian President Vladimir Putin's war was not only physical but also ideological, aimed at securing for Russia a special status that would give it the right to dominate other countries.
"Ukraine and Poland deny Russia the right to dominate, at least over us," Sikorski said. "It will not happen. It will not return."
Kosiniak-Kamysz said Russia was changing its attack tactics and increasingly using groups of jet-powered drones to overwhelm Ukrainian air defences.
"Polish air defence remains on constant alert," he said, thanking soldiers.
Interior Minister Marcin Kierwiński said Russian drone attacks near the Dorohusk-Yahodyn border crossing were being treated with the utmost seriousness.
"The situation is being monitored on an ongoing basis," he said.
"Russia is an enemy of the free world," he added.
Ukraine's air force said Russia used more than 450 drones and four Banderol drone-missiles in overnight attacks. Western regions of Ukraine were among those targeted.
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Source: IAR/PAP