The US has distanced itself from an incursion into Russia – which Moscow says ended in the defeat of armed insurgents who entered from Ukraine.
Parts of the border region of Belgorod came under attack on Monday, in one of the largest cross-border raids since Russia invaded its neighbour last year.
Russia later released pictures of abandoned or damaged Western military vehicles, including US-made Humvees.
The US insisted it did not “encourage or enable strikes inside of Russia”.
A state department spokesman acknowledged reports “circulating on social media and elsewhere” that US-supplied weapons had been used, but said his country was “sceptical at this time of the veracity of these reports”.
In a news briefing on Tuesday, Matthew Miller added: “It is up to Ukraine to decide how to conduct this war.”
Some Ukrainian military experts and bloggers have suggested that the images of destroyed US vehicles released by Russia could have been staged.
Villages in Belgorod near the border were evacuated after coming under fire. Russia says 70 attackers were killed, and has insisted the fighters were Ukrainian.
But Kyiv denies involvement – and two Russian paramilitary groups opposed to Russian President Vladimir Putin say they were behind the incursion.
Monday’s raid led Moscow to declare a counter-terrorism operation, giving the authorities special powers to clamp down on communications and people’s movements.
The measures were only lifted the following afternoon, and even then, one of the paramilitary groups was claiming it still controlled a small piece of Russian territory.
Regional governor Vyacheslav Gladkov said one civilian had died during the violence, and several others were injured.
In a later development, he said the region had been subject to a “large” number of drone attacks overnight on Tuesday. He said the attacks damaged private vehicles, houses and offices, but there were no victims.
Mr Gladkov also said a gas pipeline was damaged in the Graivoron district by the drone barrage, which led to a small fire on Wednesday morning.
The claims by the warring sides have not been independently verified – although the BBC was able to establish that a building used by Russia’s main security agency, the FSB, was among those hit during the violence. It is not clear what caused the damage.
Commenting on the hostilities in Belgorod, Russia’s defence ministry said a “unit of a Ukrainian nationalist formation” had invaded its territory to carry out attacks.
One of its photos showed a wrecked vehicle with the words “for Bakhmut” written in Russian on it, a reference to the Ukrainian city which Russia says it has recently captured – a claim disputed by Kyiv.
As well as killing dozens of what it described as “Ukrainian terrorists” in artillery and air strikes, the ministry claimed to have driven the rest of the fighters back to the Ukrainian border.
But Ukrainian officials said the attackers were Russians, from groups known as the Liberty of Russia Legion and the Russian Volunteer Corps (RVC).
Social media posts from the two paramilitary groups appeared to confirm their involvement. Both groups also told Ukraine’s public broadcaster Suspilne that they were creating “a demilitarised zone on the border with the Russian Federation from which they will not be able to shell Ukraine”.
Any assaults on Russian soil make leaders in the Nato military alliance of Western countries nervous – meaning that the developments could prove a mixed blessing for Kyiv.
The cross-border incursion may be embarrassing for Moscow, and go some way to offset the bad optics for Ukraine of reportedly losing control of Bakhmut after months of intense and bloody fighting.
It is also likely to be part of Ukraine’s shaping operations ahead of its coming counter-offensive, aiming to draw Russian troops away from the south where Kyiv is expected to attack.
But it is not a development that is likely to be welcomed by the West.
The long-range weapons these countries have provided to Kyiv – although not used in this attack – still come with the proviso they are not to be used to hit targets inside Russia.
Despite official denials from Kyiv, it is hard to believe this raid was launched without assistance from Ukrainian military intelligence.
It plays into the Kremlin narrative that Russia’s own sovereign security is under attack from malign forces backed by the West.
It is a narrative likely to be fuelled by reports that some of those who took part are linked to far-right extremism, reinforcing Moscow’s claim that it is trying to rid Ukraine of neo-Nazis.