The move came as Polish Prime Minister Donald Tusk warned that Moscow appeared poised to intensify its campaign against Ukraine's borders with European countries.
Ukraine is under mounting pressure from Russia's intensifying air campaign that uses ballistic missiles and jet-powered drones to pierce defences.
"These coming weeks and months will be a time of very intensified actions on the Russian side, and unfortunately we cannot rule out that this escalation will also affect our territory," Tusk said on Sunday after a governmental security briefing in Warsaw.
He issued a similar warning on Thursday.
Defence Minister Władysław Kosiniak-Kamysz said Monday in a post on X that the Polish army recovered what was believed to be a Russian military drone from the Baltic Sea near the coastal village of Jaroslawiec.
Polish officials said intelligence reports, including a CIA briefing last week, suggested Russia was likely to attack border points and intensify sabotage actions inside European countries as part of its efforts to discourage partners from supporting Ukraine.
Tusk said he would consult NATO allies on preparing a potential joint response.
Polish Foreign Minister Radoslaw Sikorski underscored the alliance's military edge in a social media post, saying that in the event of Russian aggression against NATO, European NATO air forces, without US participation, would be capable of destroying half of Russia's oil refineries faster than Ukraine.
Deputy Defence Minister Cezary Tomczyk described Sunday's drone strikes as a serious escalation from Russia.
He told broadcaster TVN24 on Monday that any spillover into European countries could take the form of sabotage or a sharp intensification of hybrid warfare "on a scale that we have not seen before", or other actions along NATO's borders.
The warnings followed a strike on Sunday on a train near the Ukraine-Poland border, minutes after a diplomatic delegation that included former British Prime Minister Boris Johnson and former Swedish prime minister Carl Bildt had passed through the same station, according to Ukraine's state rail operator.
A second strike hit near a separate border crossing point between Poland and Ukraine.
Kaja Kallas, the European Union's top diplomat, said Monday that the drone attacks near Poland's border were "clearly meant to scare Western countries from supporting Ukraine".
"We should show that we are there for Ukraine and we are not scared," she said.
Kremlin spokesman Dmitry Peskov, asked Monday about the strike on the train near the Polish border, said Russian forces were operating "across the entire territory of Ukraine and continues to do so - and will continue to do so".
Peskov noted the potential role of Global South nations in a settlement, saying "any country can use its influence on the Kyiv regime to encourage it to show greater flexibility".
Chinese President Xi Jinping and Indian Prime Minister Narendra Modi each expressed willingness to help broker a settlement during recent meetings with Russian President Vladimir Putin, who briefed them on the situation in Ukraine, Peskov said.
Peskov also addressed US President Donald Trump's call for Ukraine to halt strikes on Russian diesel fuel facilities, saying "any call on the Kyiv regime to stop strikes on civilian economic infrastructure can only be welcomed".
Trump on Sunday called on Ukrainian President Volodymyr Zelenskiy to halt strikes on Russian oil refineries and other infrastructure used to produce and distribute diesel, saying the attacks are causing a global shortage.
He spoke after diesel prices in the US hit a record on Friday, soaring past an average of $US6 per gallon.
