The rain will be heavy enough to produce what the National Weather Service called “life-threatening and catastrophic flooding,” along with mudslides and landslides across Puerto Rico on Monday.

More than 1.3 million customers were without power early Monday morning, according to poweroutage.us, which tracks power interruptions. LUMA, the power company, said electricity had been restored to about 100,000 customers overnight.

LUMA warned on Sunday that full power restoration in Puerto Rico could take several days, with the storm creating “incredibly challenging” conditions for repair workers. “The current weather conditions are extremely dangerous and are hampering our ability to fully assess the situation,” it said on its website.

In other developments:

• Floodwaters rose quickly as the rain fell on Sunday, with hundreds of people evacuated or rescued across the island, according to The Associated Press. Several large landslides were reported, and a bridge washed away in the central town of Utuado.

• Lee-Ann Ingles-Serrano, a National Weather Service meteorologist in San Juan, said the island was likely to see heavy showers on Monday, with several more inches of rain likely. “It will not be comparable to what we had yesterday, but it will be enough to exacerbate the problems that we have in some parts of the island,” she said Monday morning.

• Conditions could improve by Thursday or Friday, Ms. Ingles-Serrano said. But “we are still expecting flash flooding at least for the rest of the day today, and that might be extended for the next day,” she said.

• Fiona strengthened from a tropical storm to a Category 1 hurricane on Sunday morning. President Biden approved an emergency declaration for Puerto Rico on Sunday, authorizing federal agencies to coordinate disaster relief efforts.