Up to 2,000 people have been rescued from floods in and around Houston, as Tropical Storm Harvey continues to batter Texas with heavy rains.

There are reports of possible deaths in submerged vehicles, but investigations continue, Chief Darryl Coleman of the Harris County Sheriff’s Office said.

Amid catastrophic flooding, the National Weather Service (NWS) warned that conditions were “unprecedented”.

Many shelters have been opened, including in a convention centre.

There is a “flash flood emergency” across the Houston Metro area, with travel near impossible, the NWS says.

It earlier noted reports of five deaths, but only one fatality in Houston has been confirmed.

Houston Mayor Sylvester Turner has urged residents not to call emergency services unless their situation is life-threatening and they need to be rescued.

“Don’t get on the road. Don’t assume this storm is over,” he said.

Houston Bush Airport has announced that all commercial flight operations have been stopped until further notice. Houston’s other airport, Hobby, is also shut, with runways completely flooded.

Two deaths have so far been confirmed from the storm since it made landfall:

In Aransas County, where Rockport is the chief town, a person died in a house fire on Friday night

A woman died in Houston as she drove through flooded streets on Saturday

The NWS in Houston and Galveston said early on Sunday that it had recorded 24.1in (61.2cm) of measured rain in the past 24 hours.

Flooding in the Houston area is expected to worsen and “could become historic”, with “potentially significant flooding also expected in other saturated areas of south-east [Texas]”, the forecaster says.

It is advising people to move to higher ground amid “an extremely dangerous and life-threatening situation”.

Residents were warned not to try to travel unless “fleeing an area subject to flooding or under an evacuation order”.

Like Houston, the island city of Galveston was also hit by “epic catastrophic flooding” overnight, the NWS added.

•Text excerpted from a BBC report.

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