Puerto Rico battled dangerous floods yesterday after Hurricane Maria ravaged the island, as rescuers raced against time to reach residents trapped in their homes and the death toll climbed to 33.

Puerto Rico Governor Ricardo Rossello called Maria the most devastating storm in a century after it destroyed the US territory's electricity and telecommunications infrastructure.

"Part of the island is lacking communications so what we have are some preliminary assessments about 13 deaths at this juncture," Rossello told CNN.

"Right now our efforts are to make sure we have everybody safe, that we can rescue people. Our efforts have already produced almost 700 rescues so we're clearly focused on that."

The National Hurricane Center said some areas in Puerto Rico could see 40 inches (more than a meter) of rain from Maria, and Rossello warned of dangerous mudslides brought on by the deluge.

"We have a lot of flooding, we have reports of complete devastation of vulnerable housing. Of course it's still raining over here."

Maria has been blamed for at least 33 deaths, including 15 in Dominica, three in Haiti and two in Guadeloupe.

After lamenting that Puerto Rico had been "absolutely obliterated" by Maria, US President Donald Trump spoke with Governor Rossello on Thursday night when he promised to speed up emergency relief efforts.

Although the southeast coast suffered the worst damage, no part of the island escaped the storm's wrath, including the capital San Juan where there was widespread flooding.

In the Dominican Republic, the heavy rains triggered flooding as rivers overflowed their banks.