Low-lying New Orleans, devastated by 2005's Hurricane Katrina, is bracing to receive up to 10in (25cm) of rain in 36 hours, with flash floods a major risk.
The storm, which earlier achieved hurricane status, has dumped record rainfall in the region.
Large parts of the Texas city of Houston are underwater, and more than 20 people are reported dead.
Thousands of people there have fled their homes in search of emergency shelter amid severe flooding.
Houston, America's fourth most populous city, has implemented a night-time curfew to prevent looting from abandoned homes as authorities and volunteers battle to rescue stranded people and provide shelter for those made homeless by the rising waters.
The curfew runs from 00:00-05:00 local time (05:00-10:00 GMT) for an indefinite period. Relief volunteers, first responders, and those going to and from work are exempt.
The rainfall in Texas set a new record for the continental US, the National Weather Service said on Tuesday. A rain gauge in Cedar Bayou recorded nearly 52in of rain since Friday.
President Donald Trump visited Texas on Tuesday to survey the damage brought by Harvey.
He arrived in Corpus Christi, where Hurricane Harvey first made landfall on Friday, with First Lady Melania Trump.
Mr Trump said he wanted the relief effort to stand as an example of how to respond to a storm.
"We want to do it better than ever before.
"This storm, it's epic what happened. But you know what, it happened in Texas and Texas can handle anything."
He will not be visiting Houston. The White House said he did not want his visit to disrupt the emergency response.
Mr Trump has declared a federal state of emergency in both Texas and Louisiana. The move releases emergency government funding and other assistance.
Harvey was the most powerful hurricane to hit Texas in more than 50 years when it made landfall at Corpus Christi, 220 miles (354km) south-west of Houston. The storm is expected to continue dumping huge amounts of rain in the coming days over already flood-hit areas.
