US officials say two dams near Houston have begun overspilling as tropical storm Harvey pushes reservoirs past capacity.

A pair of dams near flood-hit Houston and a levee south of the city have begun overflowing, with officials in the US state of Texas warning residents in nearby areas to evacuate before water levels rise.

Harris County officials told the Reuters news agency on Tuesday that water levels in the Addicks and Barker reservoirs were at record highs, forcing engineers to release more water into the city’s swollen drainage system to alleviate pressure.

READ MORE: Hurricane Harvey – What you need to know

Engineers have been periodically releasing water from both reservoirs, but the amount of water entering exceeds the amount being released, sending floodwater over spillways.

Flood control official Jeff Lindner said on Twitter that water levels had surpassed the height of the reservoir edge, warning that more streets and homes would be flooded as a result.

#BREAKING: Addicks reservoir water level has reached 108'. Awaiting confirmation water is going over spillway for first time in history. pic.twitter.com/WQ5IzpzLzX — Travis Herzog (@HerzogWeather) August 29, 2017

Authorities in Brazoria County, an area south of Houston with a population of more than 300,000, later issued an evacuation order as a levee breached, telling residents to “get out now.”

Meteorologists have warned that the worst might be yet to come, with nearly two more feet (61cm) of rain expected on top of the 30-plus inches (76cm) in some places.

Floodwaters have already reached the rooflines of single-story homes with the US’ fourth-largest city still mostly paralysed by one of the largest downpours in history.

READ MORE: Facing Hurricane Harvey

Harvey, which has been downgraded from a hurricane to a tropical storm, has been blamed for several deaths, including a woman killed on Monday in Porter, a town northeast of Houston, when a large oak tree dislodged by heavy rains toppled onto her trailer home.

A Houston television station reported on Monday that six family members were believed to have drowned when their van was swept away.

The KHOU report was attributed to three family members the station did not identify. No bodies have been recovered.

Al Jazeera’s Heidi Zhou-Castro, reporting from Houston, said that in the last 48 hours, emergency agencies had received some 6,000 calls for help.

More than 30,000 people are expected to be placed in temporary shelters and about 450,000 are anticipated to apply for disaster assistance, which would make them eligible for financial support, possible replacement of property and other disaster-related aid.

President Donald Trump is expected to visit Texas on Tuesday, but not Houston, as flooding in the city continues.

Harvey is the first major natural disaster to hit the United States during Trump’s presidency. On Sunday, he convened a cabinet meeting by telephone in response to the disaster.

Harvey was the fiercest hurricane to hit the country in 13 years, and the strongest to strike Texas since 1961’s Hurricane Carla, the state’s most powerful hurricane on record.