New Jersey's announcement allows people who have been forced to leave their communities, as well as emergency workers working with disaster-relief efforts away from home, to do the same.
"This isn't like, 'Hell, I feel like staying at work tonight, let me fax my vote in.' No, no, no," Gov. Chris Christie told reporters Sunday. "This is if you have been displaced from your home by the storm. This is also not, 'I got evicted for not paying rent -- I'd like to vote by fax.' No."
The state is also consolidating polling places that have lost power or are cut off with others that are up and running, said Ernest Landante, a spokesman for New Jersey Lt. Governor Kim Guadagno.
In many states, remote electronic voting is already available to members of the military and U.S. citizens living overseas. But experts have raised concerns about the security of electronic voting in the past.
New Jersey officials did not explain how they will authenticate e-mails or faxes from voters. But Christie quipped Sunday that there would be "no more voter fraud in New Jersey than usual."
"Nothing's different because we're giving people different modes to be able to vote," he said. "I don't think it's any more susceptible to fraud than the system is already." And anyone who tries "better hope they don't get caught, because if they do, we'll make an example of them."
The presidential race isn't expected to be close in New York or New Jersey, both longtime Democratic strongholds in national politics.
And offshore, the Navy said it would help any sailors and Marines aboard the helicopter carrier USS Wasp who had planned to vote on Tuesday get their ballots cast. The ship had been at sea on a training mission when Sandy formed, and it was then dispatched to the New York/New Jersey area to assist with relief efforts.
Many of the roughly 1,100 aboard were registered to vote in their hometowns rather than in the counties around the ship's homeport of Norfolk, Virginia, so their votes had likely been cast and mailed already. For those registered in Virginia, the Navy is working to get them a federal write-in ballot that will be transferred back to shore, Lt. Commander Chris Servello told CNN.