Workers on the rig, in the Kab oil field in the southeastern Gulf of Mexico, jumped onto emergency rafts after the collision caused leaks in crude oil and natural gas pipes.
Carlos Morales, Pemex exploration and production chief, called the accident one of the worst in the company's history.
The death toll could rise as bad weather continues to hamper efforts by navy rescue teams to locate other workers.
Mexico's three main oil exporting ports in the crude-rich Gulf of Mexico were shut for a second day due to weather conditions - suspending oil shipments to the United States.
Port officials say it is unlikely ports will re-open before Thursday.
Pemex said US consumers of its oil supplies should not suffer as it will reschedule the delayed shipments once the storm passes.
It did not evacuate any other oil platforms or shut down production as the worst of the bad weather is seen to have passed.
The company said it would take up to five days to seal the leaking natural gas and oil but that the extent of the crude spill was less than previously thought.