Forecasters predict 50 inches of rain for parts of flood-hit Houston from Hurricane Harvey

The flooding was so widespread that authorities had trouble pinpointing the worst areas.

They urged people to get on top of their homes to avoid becoming trapped in attics and to wave sheets or towels to draw attention to their location.

As the water rose, the National Weather Service offered another ominous forecast:

Before the storm passes, some parts of Houston and its suburbs could receive as much as 50 inches of rain. That would be the highest amount ever recorded in Texas.

"The breadth and intensity of this rainfall is beyond anything experienced before," the National Weather Service said in a statement.

Average rainfall totals will end up around 40 inches for Houston, weather service meteorologist Patrick Burke said.

The director of the Federal Emergency Management Agency, Brock Long, said the government expected to conduct a "mass care mission" and predicted that the aftermath of the storm would require Fema's involvement for years.

"This disaster's going to be a landmark event," Mr Long said.

Rescuers had to give top priority to life-and-death situations, leaving many displaced families to fend for themselves. The city's main convention centre was quickly opened as a shelter.

Harris County Sheriff Ed Gonzalez used Twitter to field calls for assistance. Among those seeking help was a woman who posted: "I have 2 children with me and the water is swallowing us up."

Some people used inflatable beach toys, rubber rafts and even air mattresses to get through the water to safety.

Others waded while carrying rubbish bags stuffed with their belongings and small animals in pet carriers.

Houston Mayor Sylvester Turner said authorities had received more than 2,000 calls for help, with more coming in.

He urged drivers to stay off flooded roads to avoid adding to the number of those stranded.

"I don't need to tell anyone this is a very, very serious and unprecedented storm," Mr Turner told a news conference.

"We have several hundred structural flooding reports. We expect that number to rise pretty dramatically."

The mayor defended his decision not to ask residents to evacuate before the heavy rain from Harvey swamped roads and neighbourhoods.

He said there was no way to know which areas were most vulnerable.

"If you think the situation right now is bad, and you give an order to evacuate, you are creating a nightmare," he said, citing the risks of sending the city's 2.3 million inhabitants onto the highways at the same time.

Rainfall of more than four inches per hour resulted in water levels higher than in any recent floods and higher than during Tropical Storm Allison in June 2001, said Jeff Linder of flood control district in Harris County, which includes Houston.

The Coast Guard, which received more than 300 requests for help, deployed five helicopters and asked for additional aircraft from New Orleans.

Staff at a Houston television station broadcasting live coverage of the floods had to evacuate after water started to gush into the building.

The anchors and news operations at KHOU moved first to a second floor before finally abandoning the station.

President Donald Trump tweeted on Sunday morning that he would visit Texas "as soon as that trip can be made without causing disruption. The focus must be life and safety".

Police said a sinkhole has opened on a Texas road about 25 miles (40 kilometres) south west of Houston as Harvey dumps more rain on the region.

Rosenberg police tweeted a photo of the gaping hole that spread across more than half of a two-lane road - Farm-to-Market 762.

The 3900 block of FM 762 (in front of 24 HR fitness) has just collapsed. There is a massive sinkhole in the roadway. AVOID THE AREA! #Harvey pic.twitter.com/BJreUS1D9C

— Rosenberg Police (@RosenbergPolice) August 27, 2017

Water could be seen filling the sinkhole as pieces of road hung from the edge of the damaged roadway.

AP