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5 year oldRussia's Pacific Fleet said the cruiser USS Chancellorsville crossed just 50m (160ft) in front of the destroyer Admiral Vinogradov at 06:35 Moscow time (03:35 GMT).
It was forced to perform "emergency manoeuvring" to avoid the US ship.
But US forces blamed the Russians, claiming their ship was responsible.
US Seventh Fleet Commander Clayton Doss called the Russians "unsafe and unprofessional", saying their destroyer "made an unsafe manoeuvre against USS Chancellorsville". He dismissed the Russian allegation as "propaganda".
Admiral Vinogradov came within 50 to 100 feet (15m-30m) of the USS Chancellorsville in the Philippine Sea, the US said.
The Russian Pacific Fleet meanwhile said the incident took place in the southeast of the East China Sea, and added they had sent a message of protest to the US ship's commanders.
In a statement it said the US warship had "suddenly changed direction and crossed the path of Admiral Vinogradov just 50m away," forcing the Russian crew to make a quick manoeuvre.
By Jonathan Marcus, BBC defence and diplomatic correspondent
Two warships; two narratives - but one very real chance of accident or potential injury. There is simply no reason for vessels of this size to be in such close proximity.
One of them - or maybe even both - was at fault. Both sides blame the other. But this kind of incident is becoming ever more frequent and it does generally seem to be the result of a concerted policy by Russia to challenge US and its allies naval operations whenever possible.
Often these incidents occur in the Black Sea which Moscow sometimes regards as its own lake; a view with which other states on its shores - some of them Nato members, or aspiring Nato members - disagree.
Such incidents between the US and Russia are less frequent in Asian-Pacific waters, where the tensions tend to be between US and Chinese ships or aircraft. But wherever it occurs naval brinkmanship of this kind is dangerous and unnecessary.
Both countries regularly accuse the other of dangerous military manoeuvres - at sea and in the air.
In November, the US posted footage of a Russian jet intercepting one of its planes over the Black Sea - a move they called "irresponsible", but which the Russians said was to stop "a violation of Russian airspace".
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