The official Vietnam News reports the rig has moved east-southeast. It's accompanied by six warships, 13 cargo vessels and 19 tugboats.
The Vietnam Fisheries Surveillance Department said Chinese fishing boats in the area, accompanied by two Coast Guard vessels, have been circling Vietnamese fishing boats in what the official news agency said were traditional fishing grounds near the rig.
Tran Van Hang, chairman of the External Relations Committee at the Vietnamese National Assembly, sent a letter Tuesday to lawmakers saying China's actions were provocative.
"Peace, stability, security, maritime and aviation safety and freedom in the East Sea are being seriously threatened," his letter read.
China this week sent a letter to U.N. Secretary-General Ban Ki-moon saying the rig was deployed in its territorial waters, a claim disputed by the Vietnamese government. Beijing has said its drilling activity in the South China Sea, which began in May near the Xisha Islands, is routine.