As Trump set to visit Puerto Rico, 95 percent lack power

* Trump due in Puerto Rico on Tuesday

* Only about 5 pct of customers have power restored

* Governor: 'There is no cash on hand' (Adds resident saying conditions slowly improving, paragraphs 6-9)

By Robin Respaut and Gabriel Stargardter

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 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 during Trump's visit.

"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. He is due in Las Vegas on Wednesday to meet with people affected by Sunday's mass shooting.

For 72-year-old Angel Negroni of Juana Matos, the situation has begun to improve as flood waters receded from his neighborhood, located 20 minutes from San Juan.

Locals could occasionally get spotty cellular service, an improvement from the communication vacuum of days earlier. And he can trade his neighborhood's restored municipal water for ice made by a friend's generator-powered freezer.

"It's better now," said Negroni, while standing on his covered porch on Monday, cooking fish on a propane-powered camping stove. "We're OK."

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 on a trip to the island on Monday said things were improving with traffic moving and businesses reopening.