(Updates with Trump meets San Juan mayor, comments)
SAN JUAN, Puerto Rico, Oct 3 (Reuters) - President Donald Trump visited Puerto Rico on Tuesday on a mission to reassure the island's struggling residents that he is committed to their recovery from a devastating hurricane that has tested his ability to manage natural disasters.
One of the first people Trump met when he and his wife, Melania, touched down in San Juan, Puerto Rico, was the city's mayor, Carmen Yulin Cruz, who has repeatedly blasted Trump as showing insufficient concern about the U.S. territory's plight.
Trump, who has grappled with hurricanes Harvey, Irma and Maria in the past six weeks, praised the federal assistance so far in Puerto Rico but said at a briefing that the disasters are straining the boundaries of the U.S. budget.
"I hate to tell you, Puerto Rico, but you've thrown our budget a little out of whack because we've spent a lot of money on Puerto Rico," he said. "And that's fine, we've saved a lot of lives."
The trip offered Trump the chance to show solidarity with survivors, who are still struggling to get basic necessities, and demonstrate how his government intends to help them recover after they were hit by Maria, the worst hurricane in 90 years.
A few days earlier Trump had lashed out at Cruz on Twitter for "poor leadership" on the weekend after she criticized his government's response. He cited "politically motivated ingrates" and said some people on the island "want everything to be done for them."
Trump shook hands with Cruz after his arrival but he saved his warm words of praise for other local and federal authorities.
"Right from the beginning, this governor did not play politics," he said of Puerto Rico Governor Ricardo Rossello.
Trump's motorcade sped past trees stripped of their leaves, billboards stripped of their advertising, and the occasional home without a roof.
Not all were happy to see him.
"You are a bad hombre," said hand-lettered sign in pink marker held by a woman along the route.
Trump and his wife, Melania, met survivors of the disaster in the nearby town Guaynabo, walking down a street and talking to several families whose homes were damaged. The sidewalks were piled with debris.
"You know who helped them? God helped them. Right?" Trump said.
Later, he was to take a helicopter tour to look at the destruction. He is expected to fly over the USNS Comfort, the just-arrived hospital ship.
Before leaving Washington on Tuesday morning, Trump told reporters that roads were cleared and communication capabilities were coming back on the island. He said the mayor had "come back a long way" since her criticism.
Trump had criticism of his own about the local response.
"Their drivers have to start driving trucks," he said at the White House. "So on a local level, they have to give us more help. But I will tell you, the first responders, the military, FEMA, they have done an incredible job in Puerto Rico."
The economy of the U.S. territory, home to 3.4 million people, already was in recession and its government filed for bankruptcy in May. The storm wiped out the island's power grid, and less than half of residents have running water.
Two weeks after Maria, it is still difficult for residents to get a cell phone signal or find fuel for their generators or cars. About 88 percent of the cellphone sites are still out of service.
Valentine Navarro, 26, a salesman in San Juan, shrugged off Trump's trip as a public relations exercise.
"I think hes coming here because of pressure, as a photo-op, but I dont think hes going to help more than he has already done and thats not much," Navarro said.
Puerto Rican Governor Ricardo Rossello said that as Trump flies over the island he would see "the magnitude of the devastation." He said there were 320 functioning cash machines across the island and that waiting times for gasoline had dropped significantly.
Trump got high marks for his handling of Hurricane Harvey in Texas and Hurricane Irma in Florida and the Caribbean.
Caught off guard by the severity of Hurricane Maria's damage to Puerto Rico, Trump did not focus on the storm for days, instead launching a barrage of tweets over his view that National Football League players should be required to stand during the U.S. national anthem.
A previous Republican president, George W. Bush, faced widespread criticism for his administration's initial handling of Hurricane Katrina, which killed some 1,800 people in and around New Orleans in 2005.
Images of Trump standing together with mayors, the governor and federal officials would go a long way toward showing Americans the White House is addressing the hurricane damage, said retired Coast Guard Admiral Thad Allen.
Allen, who led the federal response to Hurricane Katrina and the Gulf oil spill, said the presidential visit will provide a chance to communicate that Americans care about the disaster on the isolated island territory.
Trump's administration has transferred more than $20.5 million in federal funds to Puerto Rico to defray disaster expenses, FEMA said on its website.
The administration is preparing to ask Congress for $13 billion in aid for Puerto Rico and other areas hit by natural disasters, according to congressional sources said.
But that money will only go so far. The island's recovery will likely cost more than $30 billion.
(Reporting by Roberta Rampton in WASHINGTON and Gabriel Stargardter in SAN JUAN, Puerto Rico; Additional reporting by Jeff Mason; Editing by Catherine Evans and Bill Trott)