* Trump due in Puerto Rico on Tuesday
* Only about 5 pct of customers have power restored
* Governor: 'There is no cash on hand' (Adds details on cell service, comment from FEMA administrator)
SAN JUAN, Puerto Rico, Oct 2 (Reuters) - President Donald Trump is set to make his first visit to Puerto Rico on Tuesday, two weeks after Hurricane Maria devastated the U.S. territory, and is likely to face more criticism of his handling of the disaster as the vast majority of the island's inhabitants lack power and phone service and are scrambling for food, clean water and fuel.
San Juan Mayor Carmen Yulin Cruz led the attack on the administration's response on Friday, criticizing an official's description of relief efforts as a "good news story" and urging Trump to act more decisively. Trump fired back at Cruz on Twitter, accusing her of "poor leadership."
It is not clear if the two will meet on Tuesday.
"She (Cruz) has been invited to participate in the events tomorrow, and we hope those conversations will happen and that we can all work together to move forward," White House spokeswoman Sarah Sanders told reporters on Monday.
Trump will spend "significant time" on the island on Tuesday, Sanders said. He is due in Las Vegas on Wednesday to meet with people affected by Sunday's mass shooting.
Early on Monday Puerto Rico's governor reported some progress in getting fuel supplies to the island's 3.4 million inhabitants as they faced a 13th day largely without power after Maria.
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.
Mobile phone service is still elusive. The U.S. Federal Communications Commission said on Monday 88.3 percent of cellphone sites - which transmit signals to create a cellular network - were out of service, virtually unchanged from 88.8 percent on Sunday.
FEMA Administrator Brock Long told reporters on a call on a trip to Puerto Rico Monday that things were improving with traffic moving and businesses reopening.
"I didn't see anybody in a life-threatening situation at all," he said. "We have a long way to go in recovery" and he said rebuilding Puerto Rico is "going to be a Herculean effort."
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. All of Puerto Rico's primary ports have reopened but many still have restrictions, according to the U.S. Department of Energy.
At least four tankers carrying fuel are waiting to unload with two more on the way, according to Thomson Reuters shipping 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.
RUNNING OUT OF CASH
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."
Trump's administration is preparing to ask Congress for $13 billion in aid for Puerto Rico and other areas hit by natural disasters, congressional sources said. The island's recovery will likely cost more than $30 billion.
(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)