* Trump due in Puerto Rico on Tuesday
* Governor: 'There is no cash on hand' (Adds detail on fuel tankers, governor's comments on financial problems)
SAN JUAN, Puerto Rico, Oct 2 (Reuters) - Puerto Rico Governor Ricardo Rossello reported progress in getting fuel supplies to the island's 3.4 million inhabitants on Monday as they faced a 13th day largely without power after the U.S. territory was devastated by Hurricane Maria.
U.S. President Donald Trump, who has faced criticism for his administration's response to the disaster, is scheduled to visit Puerto Rico on Tuesday, as food and drinking water remain in short supply.
Nearly two weeks after the fiercest hurricane to hit the island in 90 years, some residents got cell phone service back on Sunday. Others gathered at bars for drinking and dancing after a dry law was lifted this weekend.
The ramping up of fuel supplies should allow more Puerto Ricans to operate generators and travel more freely where the state of the roads allows.
"We've been increasing the number of gas stations that are open," Rossello said at a news briefing, with more than 720 of the island's 1,100 gas stations now up and running.
Puerto Rico relies on fuel supplies shipped from the mainland United States and distribution has been disrupted by the bad state of roads.
"We will be receiving more fuel supplies in the coming days," said Rossello, who is expecting some 300,000 barrels of diesel on Wednesday and 100,000 barrels of gasoline. Within the next couple of days, he expects 500,000 barrels of diesel and close to 1 million of gasoline to arrive on the island.
One of the territory's main oil ports, Yabucoa, received its first tanker on Monday after resuming restricted operations during the weekend while Ponce, another large port on the island, also resumed work, according to the U.S. Department of Energy and Thomson Reuters vessel tracking data. The island's largest port, San Juan, fully reopened on Thursday.
"The flow is coming, gasoline is getting here," Rossello said. "We have been able to reduce the time that it takes to get gasoline and diesel at different stations."
He said 8,800 people now were housed in 140 shelters. There were as many as 500 shelters in operation 10 days ago.
He said 47 percent of water and sewer service is up but there is variation across the island.
Federal and local authorities were working together to keep 50 hospitals operational and Rossello said the U.S. Navy hospital ship Comfort would arrive in Puerto Rico between Tuesday and Wednesday.
As it tries to get back on its feet, Puerto Rico is in danger of running out of cash in a matter of weeks because the economy has come to a halt in the hurricanes aftermath, Rossello told the local El Nuevo Dia newspaper in an interview published on Monday.
After filing for the largest U.S. local government bankruptcy on record in May, Puerto Rico owes about $72 billion to creditors and another $45 billion or so in pension benefits to retired workers before it even accounts for the extra expense of recovery.
"There is no cash on hand. We have made a huge effort to get $2 billion in cash," Rossello said in the interview. "But let me tell you what $2 billion means when you have zero collection: it's basically a month governments payroll, a little bit more."
It is not yet clear how the United States will help finance Puerto Rico's recovery, which likely will cost more than $30 billion. Rossello said last week his government would ask the U.S. Treasury and Federal Reserve for lines of credit at reasonable rates.
Rossello generally has praised the Trump administration's help so far, despite public criticism of the response from some officials in Puerto Rico. Ahead of his visit, Trump has defended his administration's handling of the disaster.
"We have done a great job with the almost impossible situation in Puerto Rico," he posted on Twitter on Sunday. "Outside of the Fake News or politically motivated ingrates people are now starting to recognize the amazing work that has been done by FEMA and our great Military."
Earlier, Trump attacked San Juan Mayor Carmen Yulin Cruz on Twitter after she criticized the administrations response to Maria.
The White House has not released any details on Trump's visit.
Insurers and reinsurers continued to count the cost of hurricanes this season. Lloyd's of London underwriter Hiscox Ltd estimated on Monday that it would face net claims of about $225 million from hurricanes Harvey and Irma.
The Lloyd's of London insurance market has forecast that it expects net losses for the market of $4.5 billion from the two hurricanes.
Maria alone could ultimately cause $15 billion to $30 billion in insured losses, including business interruption, according to risk modeling firm RMS. AIR Worldwide put the number at $40 billion to $85 billion.
With another two months of the Atlantic hurricane season to go, 2017 could end up as the most expensive year ever for insurers and reinsurers, if the final tally exceeds the $143 billion in losses from 2011, the year a massive earthquake and tsunami hit Japan.
(Reporting by Robin Respaut, Gabriel Stargardter, Nicholas Brown and Carlos Barria in SAN JUAN, Puerto Rico; Doina Chiacu, Roberta Rampton and Makini Brice in WASHINGTON; Marianna Parraga in HOUSTON; Rodrigo Campos and Herb Lash in NEW YORK and Esha Vaish in BENGALURU; Writing by Bill Rigby; Editing by Bill Trott)