New Jersey Governor Chris Christie said Thursday, a month to the day after the storm struck, he was upping his earlier estimates of the storm's heavy costs in his state, now putting the price at $36.9 billion.

"I've called this experience New Jersey's Katrina because the damage to our state is nothing that we've experienced ever before," Christie said, referring to a 2005 hurricane that swamped New Orleans and the US Gulf of Mexico coast.

"We have a long way to go to rebuild and restore our communities," Christie added.

His counterpart in Connecticut, Dannel Malloy, announced Thursday he was going to ask for $3.2 billion in federal aid to replace or reinforce infrastructure damaged by Sandy, as well as by Hurricane Irene in August 2011 and by a winter storm on November 7.

And on Monday, New York Governor Andrew Cuomo also revised upward his estimates of the storm's costs to his state to $41.9 billion.

Like Christie, Cuomo also compared Sandy to Katrina, though the earlier storm, which made landfall near New Orleans, killed more than 1,800 people, compared to the more than 110 killed by Sandy.

Christie said that more than 30,000 businesses and homes in New Jersey were destroyed or damaged by Sandy and that millions of households were impacted by power outages.

Some 233,000 New Jersey residents have already asked for federal assistance through the Federal Emergency Management Agency, or FEMA, he added.

In New York State, more than 305,000 homes were damaged or destroyed by Sandy, along with 265,000 businesses.

On Wednesday, New York City Mayor Michael Bloomberg came to the US capital, Washington, to lobby for billions of dollars of federal aid for his city and state.

"There's every reason for Congress to provide us with the assistance we need, given New York City's importance to the health of the entire nation," Bloomberg said.

"We're just 2.6 percent of the nation's population but we do generate 4.3 percent of America's gross annual domestic product," he added.

The October 29 hurricane flooded the subway train system, damaged tens of thousands of houses in the New York area, and knocked out electricity in swaths of the city for days, leaving many stores and businesses unable to operate.

The floods and wind also destroyed or damaged hundreds of thousands of homes, schools and hospitals, and created chaos in fuel supplies after refineries and gas stations were damaged.