The US has distanced itself from an incursion into Russia – which Moscow said 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 has insisted it did not "encourage or enable strikes inside of Russia".
Some Ukrainian military experts and bloggers have suggested that the images of destroyed US vehicles released by Russia could have been staged.
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