The United States, Britain and other Western allies, along with Ukraine’s government, are examining claims that Russia deployed a chemical agent that sickened a handful of people in Moscow’s unrelenting bid to gain complete control over the ruined Ukrainian city of Mariupol.

Pytor Andryushchenko, an adviser to the city government, said local officials believed that some chemical had been dropped by a drone on the city’s sprawling Azovstal steel plant, one of the last redoubts of the Ukrainian forces defending the city. They said it was unclear whether it was intended to be lethal.

He said that it might be something like tear gas, but that they could not be certain.

“It is absolutely correct information that yesterday from a drone, something was dropped in that area and some chemical things were in it,” he said. “But we don’t know for sure if it was poison or something else.”

Ukrainian military commanders in the city said that Russian forces had used a drone on Monday to deploy “a poisonous substance of unknown origin” that caused respiratory difficulties and neurological symptoms that can be associated with chemical agents in a handful of soldiers and civilians.

The reports, though unverified, are being treated seriously given the longstanding warnings by Western intelligence agencies that President Vladimir V. Putin of Russia might use unconventional weapons to subdue Ukrainian opposition. Having failed to seize Kyiv and quickly topple the Ukrainian government, Russia has turned its focus to Ukraine’s east and south, and defeating the remaining forces in Mariupol is essential in Russia’s effort to gain wider control over the region.

The United States, Britain and Australia said that they were monitoring the situation closely and that there would be consequences if chemical agents were indeed used.

“These reports, if true, are deeply concerning and reflective of concerns that we have had about Russia’s potential to use a variety of riot control agents, including tear gas mixed with chemical agents, in Ukraine,” the Pentagon spokesman, John Kirby, said on Monday.

The group said that at least three soldiers and civilians had been affected and that they were in “relatively satisfactory condition.” It said that the substance had been deployed close to Ukrainian military positions but “some distance” from civilian locations, and that it was “impossible to investigate the scene of the crime due to enemy fire.”

Ukraine’s deputy defense minister, Hanna Malyar, told a national television channel that the government was working to verify the information coming from Mariupol.

The British military had said earlier on Monday that Russia had previously used phosphorus munitions as weapons in eastern Ukraine, and raised the possibility that they could be used in Mariupol. Phosphorus weapons are not considered chemical weapons, and their limited use — while controversial — is not forbidden under international law.

Russia, like Ukraine and most other nations, has ratified the Chemical Weapons Convention, a treaty that bans their use. Moscow was also instrumental in pressuring Syria’s government to join the treaty in 2013 after it was accused of using a poisonous nerve agent on civilians in that country’s civil war.

But the Kremlin has sought to shield its Syrian ally from numerous accusations of chemical weapons use, calling such claims unsubstantiated or fictitious. Moscow has also been accused of using chemical agents to poison opponents including Alexei A. Navalny, the political figure. Russia denies these allegations.

On Monday, Eduard Basurin, a spokesman for the Kremlin-backed separatist Donetsk People’s Republic, described the Mariupol steel factory as a “city within a city” and said that Russian forces should “turn to the chemical troops, who will find a way to smoke the moles out of their holes.”

On Tuesday, Mr. Basurin said he had been referring to flamethrowers, not chemical weapons.