Cranes began arriving Thursday at the scene of the catastrophic bridge collapse over Baltimore harbor, as authorities shifted to a clean-up phase of the recovery and warned of extensive work before the major US port can reopen.

The machinery will be deployed in a tricky operation to clear the twisted steel remnants of the Francis Scott Key Bridge from where it fell into the Patapsco River -- blocking the entrance to the Port of Baltimore -- after a massive cargo ship Tuesday hurtled into the span.

The Army Corps of Engineers "is moving the largest crane on the Eastern Seaboard to Baltimore to help us," Maryland Governor Wes Moore told reporters Thursday evening.

Coast Guard Rear Admiral Shannon Gilreath outlined the intense work ahead: "Before we can actually engage in lifting, we've got to... figure out how to cut the bridge into the right size pieces so that we can actually lift them with the crane" out of the water.

Given the complexity and potential risks, efforts to recover the bodies of the four men still missing were called off.

"That water is so dark and the debris is so dense that, in most instances, our divers cannot see any more than a foot or two in front of them," Moore explained.

Even as crews look ahead toward recovery, "we're... incredibly sensitive to the notion that this is also the resting place for four fathers, for four brothers, for four sons," senior White House official Tom Perez told MSNBC earlier in the day.

The missing men, all Latin American immigrants, are believed to have been killed when the Singapore-flagged 1,000-foot container ship Dali lost power and careened into a bridge support column.

Nearly the entire steel structure -- crossed by tens of thousands of motorists each day -- collapsed within seconds.

The workers were part of an eight-person road repair crew on an overnight shift. Two were rescued shortly after the collapse, and two bodies were recovered Wednesday.

"Our hearts are with the families," said Moore, whose office established a relief fund to raise money for the victims' families. "We are so sorry for this tragedy."

He urged patience, adding, "This work (to rebuild) is not going to take hours, this work is not going to take days, this work is not going to take weeks."

"We have a very long road ahead of us."

Video footage from the National Transportation Safety Board (NTSB) showed investigators on Thursday boarding the disabled Dali, whose decks were covered in crumbled concrete and tangled scaffolding from the fallen bridge.

NTSB and Cost Guard officers in white hard hats are seen taking photographs and jotting down notes as they examine the rubble, before touring the intact portion of the ship.

The Federal Highway Administration said it would honor the Maryland Department of Transportation's request for an initial $60 million for what Moore called "immediate response efforts, and to lay the foundation for a rapid recovery."

"The federal government is committed to providing all necessary resources to rebuild the bridge," the agency's administrator Shailen Bhatt said in a statement.

The disaster could result in the largest marine insurance payout ever, according to the head of insurance giant Lloyd's of London, Bruce Carnegie-Brown.

"It feels like a very substantial loss, potentially the largest-ever marine insured loss, but not outside parameters that we plan for," he told CNBC.

The harbor's closure also raised concerns for the local economy -- with 140,000 jobs supported by the port -- and the wider national supply chain.

Baltimore is the biggest vehicle-handling port in the country, including cars and heavy farm equipment, according to US Transportation Secretary Pete Buttigieg. About $100 to $200 million in value comes through the port daily.

Its reopening is "our number one priority" the Coast Guard's Gilreath said.

Up the coast from Baltimore, the Port Authority of New York and New Jersey will plan to take on additional cargo to help blunt the supply chain impacts, the governors of those states pledged in a joint statement Thursday.