This article is more than
4 year oldAt least one person was killed when a tornado struck a mobile home park, officials said.
The National Hurricane Center (NHC) also warned of "the danger of life-threatening storm surge".
Isaias hammered Virginia on its way to DC, leaving 300,000 in the state without power.
It is the ninth named storm of the year.
Isaias was downgraded to a tropical storm after hitting islands in the Caribbean last week, but was re-categorised as a category-one hurricane as it approached the Carolinas on Monday.
It was then downgraded again to a tropical storm, but storm surge warnings remain in effect along the coast.
As of Tuesday morning, Isaias was moving north at 33mph (54km/h), the NHC said, with maximum sustained wind speeds of 70mph (110km/h)
Strong winds, with gusts reaching hurricane force, are expected all along the Mid-Atlantic coast and as far as New England on Tuesday.
The NHC says it is now moving quickly up the eastern seaboard. As of Tuesday morning, local time, the centre of the storm is moving across south-eastern Virginia with strong winds, heavy rains and the threat of tornadoes, according to the NHC.
A tropical storm warning remains in effect up the northeast coast all the way to Maine, with major cities like Washington, Philadelphia and New York in the potential path. By Tuesday morning, the Mid-Atlantic coast was experiencing heavy rains with warnings of flash floods spanning from Maryland to Pennsylvania.
Tornadoes are still possible from Virginia to New Jersey through Tuesday afternoon, and from New York to New England in the afternoon and evening, the NHC said.
In New Jersey, Governor Phil Murphy declared a state of emergency starting at 05:00 local time on Tuesday, closing all state offices and asking residents to stay home.
In neighbouring New York, state authorities have deployed emergency supplies including pumps, chainsaws, bottled water and sandbags throughout the state. Governor Andrew Cuomo on Twitter asked New Yorkers to exercise caution and avoid unnecessary travel, especially for those in the storm's path.
North Carolina Governor Roy Cooper, who on Friday declared a state of emergency, has also urged residents to be on the alert.
Speaking to ABC's Good Morning America programme on Tuesday, Mr Cooper said some 355,000 residents were without power. He confirmed at least one death and a number of injuries after a tornado hit a mobile home park in the north-eastern part of the state.
"All in all this storm got in [and] got out pretty quickly and that's a good sign for potential river flooding which we hope will not be serious," Mr Cooper said.
"We're of course saddened by the one fatality that we know, at least, that we have, but we know overall [with] this storm moving quickly, that the damage was not any way as great as it could have been."
The governor said things were a "little chaotic right now" but that the state was able to handle the situation. He also noted North Carolina was able to follow social distancing measures in relief efforts where needed.
State officials in regions preparing for hurricanes this season have also been grappling with opening shelters that comply with social distancing regulations.
Over the weekend the storm churned past Florida.
In the Dominican Republican and Puerto Rico, Isaias killed at least two people. It uprooted trees, destroyed crops and homes and caused flooding and landslides.
US disaster agencies have updated preparedness and evacuation guidance in light of Covid-19.
The Centers for Disease Control recommends families add Covid-19 items to a disaster "go kit" that can be taken in an emergency situation:
Here are some key guidelines for protecting yourself against Covid-19 if you must evacuate to a shelter:
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