(Corrects to show temporary cell sites are in addition to 8 million calls, 4 million texts per day in paragraph 7)
By Nick Brown and Robin Respaut
FAJARDO, Puerto Rico, Oct 2 (Reuters) - Puerto Ricans exasperated by the patchy U.S. relief response to their hurricane-blasted island are turning to a Mexican billionaire's mobile phone network they say has been faster to restore service.
Claro Puerto Rico, a subsidiary of America Movil owned by Carlos Slim, has stepped up to a challenge in the wake of Hurricane Maria that U.S. peers like AT&T Inc, T-Mobile US Inc and Sprint Corp have been slower to address, residents said.
By Saturday, 11 days after Maria hit, Claro, the island's No. 2 cellular operator, had restored service in 28 of the island's 78 municipalities, reaching about 310,000 customers.
"Claro is the only one with service here," said Francisco Portales, 47, a customer of privately held Puerto Rico-based network provider Open Mobile who was waiting outside the Claro store in Fajardo hoping to buy a phone to call his wife, whom he has heard from just once since the storm.
The coverage picture on Puerto Rico overall remains dire, with 88.8 percent of the island's cell towers out of service as of Sunday, according to the latest U.S. Federal Communications Commission update.
AT&T, the commonwealth's biggest wireless provider, T-Mobile and Sprint did not disclose how much of their networks are up and running.
AT&T, however, said on Monday its sites were carrying 8 million calls and 4 million texts per day in addition to 100,000 calls and 500,000 text for the last three days on temporary cell sites.
AT&T expects more equipment and staff to arrive shortly.
The lack of commercial power remains a significant problem, he added.
Claro said it had power generators, diesel, batteries and vehicles ready 72 hours ahead of the storm.
In contrast, AT&T had readied fuel supplies, but "could not pre-stage recovery assets in fear that they would be lost," Joan Marsh, the company's executive vice president of regulatory and state external affairs, said in a Sept. 28 blog.
Sprint said on Friday its towers were still standing and "largely intact" and that it was working to restore power and connections to towers in the most populous areas.
T-Mobile said on Sunday it is making progress with repairs and service but that "it's going to be a long road to recovery." It said it had prepared portable generators and fuel for any permanent generators.
Verizon Communications Inc, the biggest U.S. cellular provider, does not have its own network in Puerto Rico, providing service through a roaming agreement with Claro.
Sprint said it had shipped some spare parts to Puerto Rico needed for network restoration ahead of earlier Hurricane Irma.
Wireless providers say they are coordinating service restoration efforts and opening their networks to each other's customers. Activating a roaming service will connect a phone to whatever network is available.
Claro is winning supporters like Mercedes Saldana, a 54-year-old school cafeteria worker and Sprint customer. She had no service and joined friends seeking to buy a Claro prepaid phone.
"I don't have any service, none," she said. "We don't know when Sprint's going to be connected again."
AT&T has a 34 percent share of the island's active wireless numbers, according to research firm Sharetracker. Claro is second with a 26 percent share, followed by T-Mobile with 19 percent, Open Mobile with 11 percent and Sprint with 10 percent.
Luis Pacheco, 64, spent more than an hour in line to shop at a Fajardo Walmart. He was planning to drive with his wife to Canovanas - 30 to 40 minutes west - in hopes of finding a cell signal to text his daughter in California.
Choking up, Pacheco said Canovanas was the only place he knew of where his carrier, AT&T, has a signal. (Additional reporting by Gabriel Stargardter in San Juan, Puerto Rico,; Sinead Carew in New York and Jon Herskovitz in Austin, Texas; Editing by Lisa Shumaker and James Dalgleish)