* Trump due in Puerto Rico on Tuesday
* Governor: 'There is no cash on hand' (Adds details on funding request, Trump visit)
SAN JUAN, Puerto Rico, Oct 2 (Reuters) - Puerto Rico's governor 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, will make his first post-hurricane visit to the island on Tuesday as food and drinking water remain in short supply.
His administration is preparing to ask Congress for $13 billion in aid for Puerto Rico and other areas hit by natural disasters, congressional sources said, while the U.S. territory worried about running out of cash. The island's recovery will likely cost more than $30 billion.
Nearly two weeks after the fiercest hurricane to hit the island in 90 years, everyday life was still severely curtailed by the destruction. The ramping up of fuel supplies should allow more Puerto Ricans to operate generators and travel more freely.
"We've been increasing the number of gas stations that are open," Governor Ricardo 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.
Within the next couple of days, Rossello expects 500,000 barrels of diesel and close to 1 million barrels of gasoline to arrive on the island. The ports of Yabucoa, Ponce and the largest port San Juan have resumed operations, according to the U.S. Department of Energy and Thomson Reuters vessel tracking data.
"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 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.
At least 5.4 percent of customers in Puerto Rico had their power restored by mid-morning on Monday, according to the U.S. Energy Department, with San Juan's airport and marine terminal and several hospitals back on the power grid. It said the head of Puerto Rico's power utility expects 15 percent of electricity customers to have power restored within the next two weeks.
OLIVE BRANCH TO MAYOR
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."
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 administration's response to Maria.
Trump will spend "significant time" on the island Tuesday, White House spokeswoman Sarah Sanders told reporters, while noting that they had reached out to Cruz.
"She's been invited to participate in the events tomorrow, as well, and we hope those conversations will happen and that we can all work together to move forward," Sanders said.
(Reporting by Robin Respaut, Gabriel Stargardter, Additional reporting by Nicholas Brown and Carlos Barria in SAN JUAN, Puerto Rico; Doina Chiacu, Roberta Rampton, Tim Ahmann 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 and Mary Milliken; Editing by Bill Trott and Lisa Shumaker)