The move marks a fresh escalation of the dispute that erupted after China deployed the giant Haiyang Shiyou 981 rig seven weeks ago into waters Hanoi claims.
The row has seen a wave of deadly anti-Chinese riots in Vietnam as well as accusations from both sides of ramming by the other's vessels.
Talks in Hanoi between Chinese State Councillor Yang Jiechi and Vietnamese Foreign Minister and Prime Minister Nguyen Tan Dung over the dispute ended in deadlock on Wednesday.
The three other rigs -- Nanhai 2, 4 and 5 -- have already arrived at their destinations and will conduct drilling operations over the next four to eight weeks, the administration said.
Some of the positions it gave for them are east of Hong Kong and far from any area claimed by Vietnam, but it remains unclear whether the others will be deployed in disputed waters.
Chinese foreign ministry spokeswoman Hua Chunying said Friday that the rigs' operations would take place "in coastal waters of China's Guangdong and Hainan provinces" at the southern tip of the country.
General Nguyen Quang Dam of Vietnam's Marine Police told the country's state-run Thanh Nien newspaper that the Nanhai 9 was heading for a position "in the same area where China installed some rigs around five years ago, which are still operating now".
"We are closely monitoring the situation and have already prepared measures to deal with the different scenarios that could happen," he said.
In a report today on the dispatch of the rigs, China's state-run Global Times newspaper noted that about 90 percent of China's foreign trade is conducted by sea.
