North-Atlantic Treaty Organisation Secretary General Jens Stoltenberg on Tuesday extended condolences to Polish President Andrzej Duda after the explosion in the east of the country, adding that the alliance is 'monitoring the situation'.
On Tuesday, media reports said two Russian missiles landed within Polish territory near the border with Ukraine.
Top NATO and United States officials have said they are looking into reports of Russian missiles falling within the territory of the NATO member.
'Spoke with President Duda @prezydentpl about the explosion in #Poland. I offered my condolences for the loss of life. #NATO is monitoring the situation and Allies are closely consulting. Important that all facts are established,' Stoltenberg tweeted.
In its immediate reaction, the United States said stressed there is a need to gather the facts of the situation before jumping to any conclusions about missiles possibly hitting Poland.
"We want to deal with facts," Pentagon Press Secretary Pat Ryder said during a press briefing.
"I think it's incumbent on all of us to get the facts before we start speculating or jumping to conclusions."
The Pentagon press secretary said the US does not have information to corroborate reports on Russian missiles.
In a separate press conference, US State Department principal deputy spokesperson Vedant Patel said the US considers that it is important to determine whether the reported missile strikes inside Polish territory were intentional or accidental.
"Of course, that is something that would be of importance," Patel said on Tuesday when asked if the issue of whether the reported missile strikes were intentional or accidental will be considered in talks with the allies.
Earlier, the Russian news agency Sputnik said two rockets fell in the populated area of Przewodow in the Lublin Voivodeship on the border with Ukraine.
Two people were killed in the incident, the police and the army are working on the scene of the incident.
Poland's prime minister Mateusz Morawiecki convened a meeting of the Security Council Committee of the Council of Ministers after reports of missiles falling on the territory of the country.
Western media outlets said two stray rockets that landed in Polish territory came from Russia.
The Russian Defence Ministry dismissed Polish media reports about the fall of Russian missiles in Poland, adding that the its military has performed no strikes targeting the Ukrainian-Polish border zone.
'Polish mass media and officials commit deliberate provocation to escalate situation with their statement on alleged impact of 'Russian' rockets at Przewodow,' the Russian ministry was quoted as saying by TASS news agency.
"Russian firepower has launched no strikes at the area between Ukrainian-Polish border."
Poland is a member of the NATO military alliance.
Article 5 of the treaty says that if an armed attack occurs against one of the member states, it shall be considered an attack against all members.
US lawmaker Elaine Luria has urged calm amid calls to invoke NATO's collective defence pact.
'Those calling for NATO to invoke Article 5 after the attack in Poland, do not understand NATO and should not be taken seriously. Russia is losing the war, and unless this was a deliberate attack, calm is required,' Luria tweeted.