NEW ORLEANS (AP) — Ships began crawling up the Mississippi River at New Orleans in a tightly controlled procession Friday, two days after a massive oil spill shut down a stretch of one of the nation’s most critical commercial arteries.

The pecking order was based on Coast Guard determination of the economic importance of the ships’ cargo, and the pace was slowed by a scrubbing process to remove oil from each hull. A ship carrying refinery-bound oil was the first to get the go-ahead.

With more than 200 ships to be cleared, it was expected to take days to clear the backlog that developed after the tanker Tintomara collided with a barge in the early morning hours Wednesday. About 419,000 gallons of fuel oil spilled from the barge into the Mississippi at New Orleans.

The shutdown of a 100-mile stretch of river to the Gulf of Mexico halted vessels ranging from oil supertankers to grain barges in one of the world’s busiest ports. Gary LaGrange, executive director of the Port of New Orleans, said a recent economic impact study conducted by the port showed that such a total shutdown could cost the national economy up to $275 million per day.

The first ship to head north from the river’s mouth, the Overseas New York, was cleared to sail to the refinery corridor that lines the river between New Orleans and Baton Rouge.

Traffic-copping the situation was a Coast Guard unit established after Katrina to handle river shutdowns, said Coast Guard Capt. Lincoln Stroh. The unit is consulting with the shipping industry over the order of movement but has final say.

Coast Guard and industry officials hadn’t begun to tally the costs of the shipping interruption or cleanup.

The spill had sparked fears of widespread environmental damage. But crews moved in to contain the fuel oil, which pooled fortuitously in the bends of the river.

State authorities were optimistic damage could be contained.

A cleaning station was set up near the river’s mouth to scrub the hulls of vessels on their way to the Gulf. Another was being set up on the river near the New Orleans suburb of Westwego. Officials said high-pressure water would be applied to the ships’ hulls at the water line to remove oil — a process that would take three to four hours per ship.

Refineries adjusted to the shutdown. Royal Dutch Shell PLC, for example, said its Gulf Coast sites were operating as usual and meeting supply obligations. One refinery was sending some fuel by pipeline that normally would be transported by vessel.

About 2,000 passengers on a cruise ship diverted to to Mobile, Ala., were being bused to New Orleans, said its operator, Carnival Corp.

Divers inspected the wrecked barge, which is wedged against supports for the Mississippi River bridge but not considered a hazard. Stroh said little fuel oil was believed to remain. It’s unclear when efforts to raise the barge might begin.

The spill was the largest in the Mississippi River since a tanker ran aground in 2000 about 40 miles south of New Orleans, dumping more than half a million gallons of crude oil. That spill closed about 26 miles of the river.

Authorities are investigating the cause of the crash, and said there wasn’t a properly licensed pilot aboard the tugboat pushing the barge. Officials would say only that their probe is continuing.

Meanwhile, residents filed a suit Friday against the owners and operators of the vessels, alleging that they were exposed to fuel oil fumes. State officials have said tests showed that the air was safe to breathe.

A fuel odor hung in the air in the French Quarter Thursday. By Friday, morning diners at the Cafe du Monde near the French Quarter riverfront were sipping coffee, and the aroma of beignets, a fried and sugar-powdered pastry, had replaced the fuel smell.

Still, the riverboats Natchez and Creole Queen, which carry tourists on daily tours along the river, awaited Coast Guard approval to sail.

‘‘There’s a lot of disappointed people,’’ said Jamie Messersmith, manager for the Natchez steamboat. ‘‘One couple was married on the Natchez and they came for their anniversary,’’ he said.