SAN JUAN, Sept 18 (Reuters) - Most of the island of Puerto Rico was without power on Sunday as Hurricane Fiona made landfall, causing severe flooding and landslides before barreling toward the Dominican Republic, a government agency said.

The center of the storm made landfall on the southwestern coast of Puerto Rico near Punta Tocon at 3:20 p.m. ET (1920 GMT) with maximum sustained winds of about 85 miles (140 kilometers) per hour, clearing the threshold for a Category 1 hurricane, the National Hurricane Center said.

The NHC said the storm was causing "catastrophic flooding" by early Sunday evening.

By Sunday night aid agencies in the Dominican Republic began evacuating residents from high-risk areas in the east of the country. President Luis Abinader, the Dominican leader, postponed a trip to New York to participate in the United Nations General Assembly, while the start of the Dominican school year was pushed back to Wednesday, from Monday.

In Puerto Rico, electricity was initially completely out across the island of 3.3 million people, said LUMA Energy, operator of the island's grid, and the Puerto Rico power authority, on Sunday afternoon. That night officials said some power had begun to be restored, but reconnecting the whole island would take days.

Puerto Rico's grid remains fragile after Hurricane Maria in September 2017 caused the largest blackout in U.S. history. In that Category 5 storm, 1.5 million customers lost electricity with 80% of power lines knocked out.

At a press conference in the capital San Juan on Sunday night, LUMA spokesman Abner Gomez said the entire electrical system had first been shut down to protect its infrastructure. Some power was being restored with priority being given to hospitals and other critical community services, he said.

"This has been catastrophic," Puerto Rico Governor Pedro Pierluisi said at the news conference. "We are responding to the emergency as weather conditions permit."

Several landslides had been reported, officials said. Roads were closed and a highway bridge in Utuado, a town in the center of the island, had been washed away by a flooding river.

Puerto Rico's ports have been closed and flights out of the main airport canceled. Torrential rains and mudslides were also forecast for the Dominican Republic as the storm progresses northwestward, with the Turks and Caicos Islands likely facing tropical storm conditions on Tuesday, the NHC said.

U.S. President Joe Biden approved an emergency declaration for Puerto Rico on Sunday, a move that authorizes the Federal Emergency Management Agency to coordinate disaster relief and provide emergency protective measures.