Limited service will resume Thursday on New York's subway trains, state Governor Andrew Cuomo said Wednesday, with lower Manhattan still cut off because of ongoing power outages.

"Limited New York City subway service supplemented by a bus bridge from Brooklyn to Manhattan will begin tomorrow," Cuomo told a news conference.

"There will be no service in Manhattan below 34th street because there's no power for that service below 34th," he added.

The Metropolitan Transportation Authority chairman Joseph Lhota told CNN that 14 of the MTA's 23 lines would be running on Thursday.

"So I think the system, while limited, will be robust enough that millions of our passengers will be able to use it," he said.

The underground transport system was shut down ahead of Hurricane Sandy and suffered significant damage during the storm after being flooded in some places.

Lhota said tens of millions of gallons of water were being pumped out of the subway system adding, "we're going to do everything we can to get the water out before this weekend."

He said the water being pumped from the system seemed comparatively clean.

"So from that point of view I'm not worried about the environmental issue."

Bus service in New York has already been largely restored, with the city offering passengers free rides as residents struggle to get around.

However, heavy traffic has made for slow journeys and New York Mayor Michael Bloomberg announced Wednesday afternoon new rules preventing vehicles with fewer than three people from entering Manhattan over the East River.

"The streets just cannot handle the number of cars that have tried to come in, so I've ordered that the four East River bridges be restricted to high occupancy vehicles only tonight, coming into Manhattan, meaning three or more people," he said.

The restrictions will continue through Thursday and Friday until midnight.

"The bottom line is the streets can only handle so much, hopefully we can find ways for you to pick up people who will be standing by the bridges," he said.

"You're their solution and they're your solution as well."

But there was also some good news for commuters coming from outside New York. Cuomo said earlier there would be "limited commuter rail service on Metro North and on the Long Island Railroad which will begin at 2:00 pm today."

An estimated 8.5 million people use the Metropolitan Transport Authority commuter networks daily and Lhota told CNN that the storm's impact was the biggest disaster the transport system had ever experienced.

"New York City has never experienced anything like this," he said, saying the storm had reminded him of the paralysis that followed the September 11, 2001 attacks.

"What's different though is this is not isolated to the World Trade Center area and just lower Manhattan. It's citywide. The devastation that's happened on Long Island, that's happened in New Jersey, this was massive."