Heavy rains unleashed by Alex, the first hurricane of the Atlantic season, caused the deaths of at least seven people in northeast Mexico, the Nuevo Leon state governor said on Friday.

Alex was downgraded to a tropical storm just hours after roaring ashore late Wednesday as a Category Two hurricane south of the eastern US-Mexico border, in Tamaulipas state.

But heavy rainfall caused mayhem as the storm weakened across northeast Mexico, with rivers gushing beyond their banks, trees uprooted and buildings losing their roofs.

"We've had reports of seven people who sadly lost their lives in situations directly or indirectly linked to the storm," Governor Rodrigo Medina told a news conference.

More than 10,000 people were still suffering power and water cuts across the state on Friday, where the collapse of electrical cables caused some transformers to explode.

At least 11 people were killed last weekend when Alex passed through Mexico's Yucatan peninsula, Nicaragua, Guatemala and El Salvador.

Alex also disrupted clean-up operations for the massive BP oil spill in its passage through the Gulf of Mexico.

It dissipated over the mountains of central Mexico on Friday, after causing the heaviest rains in a century in Mexico's northern city of Monterrey.

The Interior Ministry on Friday declared a state of emergency in 21 towns in Nuevo Leon, allowing the use of federal funds toward damages.