The tense confrontation came as China moved its deep-sea rig to a new location earlier this week that Hanoi considers is still within its territory.
"When we approached (the Chinese warships guarding the rig) they uncovered their guns, turned them and pointed them at the Vietnamese vessels," Ha Le, deputy chief of Vietnam's Fisheries Surveillance Department, told AFP.
Japanese media meanwhile reported a standoff during which at least eight Chinese ships surrounded and trained their machine guns on a Vietnamese coastguard boat, just six kilometres from the rig.
The report said that at least 100 Chinese ships had been in the area as Chinese jets flew overhead.
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Vietnamese and Chinese vessels have engaged in increasingly tense skirmishes over the rig in the South China Sea that have triggered international alarm.
On Tuesday, Vietnam accused a Chinese ship of ramming and sinking one of its fishing boats -- the first ship reported sunk since the dispute flared in early May.
The confrontations have included reported rammings and the use of water cannon. Vietnam says dozens of people have been injured in the clashes.
Japan and the Philippines also have tense disputes at sea with China.
Vietnam's Prime Minister Nguyen Tan Dung today said that skirmishes were inevitable but "we must be restrained," according to state media.
He said at least 30 Vietnamese ships had been damaged by Chinese vessels.
Beijing, which claims nearly all of the South China Sea, blames Vietnam for the standoff, saying that the rig is in its own waters.