Houston mayor Sylvester Turner said 40 boats would be added for rescuing people from high waters that have filled neighbourhoods and highways. "Don't get on the road. Don't assume this storm is over," Mr Turner said.
Harvey came ashore late Friday as the most powerful hurricane to hit Texas in more than 50 years and has been linked to at least two deaths. The death toll is expected to rise as the storm lashes the US state for days, triggering more floods, tidal surges and tornadoes.
The centre of the storm is about 200km southwest of Houston, the fourth most populous city in the United States, and is expected to arc slowly toward Houston, bringing heavy rains, until Wednesday.
Like Houston, Galveston was also hit by "epic catastrophic flooding" overnight, the National Weather Service (NWS) said.
Several deaths have been reported. One fatality in Houston has been confirmed, of a woman who died as she drove through flooded streets.
On Friday night, a man died in a house fire in the town of Rockport, 48km north of the city of Corpus Christi. Another dozen people in the area suffered injuries including broken bones, another official said.
Harris County sheriff Ed Gonzalez said his deputies had also responded to unconfirmed reports of a deceased woman and child inside a submerged vehicle on a highway near Houston. Another resident told a local TV station of seeing a woman's body floating in the streets during a flash flood in west Houston.
Emergency services told people to climb onto the roofs of their houses rather than into their attics to escape rapidly rising waters. Authorities warned the city's more than two million residents not to leave flooded homes because many of the city's roads were underwater.
Houston police officials said officers were evacuating two flooded apartment complexes.
Rescue efforts are being hampered by strong winds and thousands are without power. The US Coast Guard in Houston has requested more helicopters as more people ask for help.
Governor Abbott has mobilised 1800 military personnel to help with rescue and repair operation
The coastal town of Rockport took a direct hit from the storm, as it made landfall as a category 4 hurricane, leaving streets flooded and strewn with power lines and debris on Saturday.
The storm ripped off roofs, destroyed buildings, flooded coastal towns and had cut off power to nearly 230,000 people in Texas as of Saturday night.