President Joe Biden will visit Louisiana later this week to inspect the damage caused by Ida, the White House said Wednesday.
The White House said Mr Biden has been receiving regular updates on the storm and that he "would absolutely not" visit Louisiana if his presence distracted from ongoing relief efforts there.
The death toll rose to at least six on Wednesday.
The National Weather Service warned of “widespread and potentially life-threatening flooding" in the north-east and mid-Atlantic.
The cities now under flash flood warnings include Philadelphia, Washington DC and Baltimore. New York and Hartford, Connecticut could also be affected.
Louisiana saw some small signs of progress on Wednesday as power returned to a sliver of New Orleans and crews began to clear fallen trees and debris from roads.
Power company Entergy said it is slowly adding power back to New Orleans just days after Hurricane Ida made landfall. An unspecified number of customers in eastern New Orleans had power turned back, the company said on Wednesday.
There are still hundreds of thousands of homes and businesses without power, from the New Orleans area to Baton Rouge, according to the state Public Service Commission. Full restoration will take weeks.
Powering up the rest of the area “will still take time given the significant damage” to the power grid, Entergy said.
More than 705,000 people statewide are also without running water, the Louisiana Department of Health said Wednesday.
At least two people in Mississippi were killed and 10 others injured late on Tuesday when their vehicles drove into a large, muddy pit following torrential rain from the powerful hurricane Ida that resulted in part of a highway being washed away.
Officials believe that heavy rainfall may have resulted in the collapse of two-lane Mississippi Highway 26 west of Lucedale town, and the drivers may not have seen that the road in front of them had disappeared.
Police said several cars fell into a hole that was 15 to 18 metres long.
Since Sunday, Mississippi has been battered by torrential rain from Ida, which made landfall in Louisiana as a Category 4 storm on Sunday. It led to flash flooding in and around Lucedale.
The area had seen 10 to 13 inches of rain since the storm began, with isolated higher amounts, according to satellite images. The National Weather Service said that two inches of rain an hour were falling in the area.
Meanwhile, Louisiana faced widespread power outages and flooding as officials examined the damage caused by Hurricane Ida, which first struck the state on Sunday.
In Louisiana, a man died while attempting to drive across a flooded area of New Orleans. Another man died after being struck by a tree near Baton Rouge.
Many people in South Louisiana have felt suffocated amid the summer heat, and are braced for a month without electricity and reliable water supplies after the hurricane.
The death toll from the hurricane is expected to rise in the coming days, Louisiana Lieutenant Governor Bill Nungesser said.
“Knowing that so many people stayed behind in places like Grande Isle and Lafitte where flood waters have devastated those areas, we expect there will be more people found who have passed,” Mr Nungesser said.
New Orleans officials have imposed a citywide curfew as large parts of Louisiana and Mississippi remain without power.
The curfew starts at 8pm at night and ends at 6am the next morning, Mayor LaToya Cantrell said, as police reported several incidents of lootings in the city.
Residents are being warned that it could take weeks until power supplies are restored in some areas.
Mayor Cantrell said she was hopeful “that we should have some level of transmission” by Wednesday but “that does not mean we will immediately see all the lights on in the city.”
Federal officials say that some 441,000 people in 17 parishes across the region have no water, and a similar number may be without power for up to a month.
The Hurricane’s heavy rains forced the Bonnaroo Music and Arts Festival in Tennessee to be cancelled as organisers said the waterlogged festival grounds were unsafe for driving or camping.
The annual festival was scheduled to start on Thursday on the site of a former farm in Manchester, about an hour south-east of Nashville.
Authorities across the south urged residents not to return home amid warnings of a storm surge and heavy rain.