By Alwyn Scott and Andrea Shalal-Esa

(Reuters) - U.S. regulators approved on Friday a revamped battery system for Boeing Co's 787 Dreamliner, a crucial step in returning the high-tech jet to service after it was grounded in January because its lithium-ion batteries overheated.

The Federal Aviation Administration (FAA) approval of design changes allows Boeing to immediately begin making repairs to the fleet of 50 planes owned by airlines around the world.

The FAA action all but ends a grounding that has cost Boeing an estimated $600 million, halted deliveries and forced some airlines to lease alternative aircraft. Several airlines have said they will seek compensation from Boeing, potentially adding to the plane maker's losses.

The agency also said the jet retained permission to fly up to 180 minutes over remote areas and oceans once U.S. regulators allowed the Dreamliner to return to the skies. There had been talk of scaling back the approved range, known as ETOPS, which would have limited the use of the fuel-efficient jet.

Boeing Chief Executive Jim McNerney said the 787's promised benefits "remain fully intact" and reaction in the industry was joyous.

FLYING AGAIN IN DAYS?

"We're back in business, baby!" tweeted the Washington Aerospace Partnership, a group of business, labor and local government leaders supportive of Boeing.

"This is a good step forward," United Airlines said in a statement. United is the only U.S. carrier with 787s and plans to add them to its schedule starting May 31. Plans to launch service from Denver to Tokyo Narita are set for June 10, but depend on completing the modifications by then, it added.

In theory, the planes could be carrying passengers again within a week. Boeing said it takes five days to refit each jet and that no regulatory barrier prevents airlines from putting planes into service after the work is finished. In practice, however, airlines typically perform "check flights" before carrying passengers, Mike Sinnett, chief 787 program engineer, told a news conference Friday.

With 10 teams already in place around the world and Friday's approval to begin work, installation could move quickly and then "it's up to the airlines" when they begin using the plane, Sinnett said.

The FAA said it will issue an "airworthiness directive" next week that formally lifts the U.S. ban on passenger flights.

Nearly half of the planes in service are owned by Japanese carriers All Nippon Airways and Japan Airlines. Japan's Civil Aviation Bureau (CAB), the counterpart of the FAA, gave a nod to the FAA's approval.

"We are closely working with the FAA and are analyzing and assessing the 787 improvement measures, and we do not see any problems," Shigeru Takano, an official at the CAB, said.

The next step for Japan would be to revise its version of the airworthiness directive, known as a "technical circular directive" Takano said that could come on or after April 25.

"We want to make the final decision on flight resumption based on the FAA's airworthiness directive revision as well as checking the results of a U.S. National Transportation Safety Board-hosted hearing set to take place on April 23 and 24," he said.

The National Transportation Safety Board (NTSB), the top U.S. transportation investigator, is investigating a battery fire on a JAL Dreamliner plane parked at an airport in Boston in January and will have an investigative hearing on the jet's battery next week.

Japan has yet to decide whether it should require ANA and JAL to take additional measures to ensure the safety of the lithium-ion batteries used in the Dreamliner, Takano added.

Mark Rosenker, who headed the NTSB under President George W. Bush, said the FAA clearly believed that Boeing's proposed changes would avert further problems.

"It should give the flying public a sense of safety and reliance and well-being," said Rosenker. He said he expected airlines to resume flying the planes in May.

COSTS STILL UNCLEAR

Much of the design change in the battery system already is well-known, thanks to Boeing's detailed descriptions of the system to customers, legislators and media.

Before the planes can fly, they must be fitted with a "containment and venting" system for both lithium-ion batteries on the 787, the FAA said. That includes a stainless-steel enclosure to prevent heat, fumes or fire from spreading if a battery overheats in flight. Batteries and battery chargers must also be replaced with different components, the FAA said.

Boeing also will install the new system on planes produced since the grounding that were barred from being delivered. "They're running out of space on the tarmac," outside the factory near Seattle, said Congressman Rick Larsen, a Washington Democrat who has the factory in his district. He said Boeing expects it will take five or six months to clear that backlog.

He said he did not have a problem with the FAA approving the fix before the NTSB hearing next week, since accident investigations often take longer than regulatory action. "There's a lot more we need to learn about lithium-ion batteries and technology," he said.

Sinnett said Boeing still expected to deliver all of the Dreamliners it had planned this year. The company has been conducting flight tests of the new planes so they can be delivered quickly when the new systems are installed.

But costs remain unclear. Boeing has not put a dollar figure on the battery crisis, but some analysts estimate it cost $50 million a week. Others said that seemed high.

Richard Aboulafia, aviation analyst at Teal Group, said Boeing also faced claims from airlines for the grounding, which would compound the much-higher-than-expected cost of launching the new aircraft. Boeing had expected to spend about $4 billion to $5 billion on the new composite plane, but the cost was now closer to $20 billion, he said.

"This has just been another increment of pain on top of a whole lot of other pain," Aboulafia said.

Nevertheless, Boeing's stock rose 2.1 percent on Friday to $87.96, and has gained 18.3 percent since the 787 was grounded on January 16.

In approving the change, the FAA is indicating that it believes Boeing's fix is adequate to address the risk of fire on the plane. However, the NTSB continues to investigate what caused a battery to catch fire on the JAL plane in Boston. A second battery overheated during an ANA flight in Japan a few days later, prompting regulators to ground the Dreamliner.

Boeing has said its redesign addresses more than 80 potential causes, and therefore is more rigorous than if a single cause had been found.

The NTSB said Friday it would call officials from the FAA and Boeing, including Sinnett, to testify, along with people from Thales SA of France, which makes the battery system, and GS Yuasa Corp of Japan, which makes the battery.

Asked Friday why Boeing trusted engineering assumptions that were proved wrong by events, and why Boeing or the public should trust them now, Sinnett said the company had learned to be more conservative in testing batteries, and applied that to the new system. He said the NTSB hearing next week would look into the question of whether the original system should have been safer.

As for other "unknown unknowns" that may lurk in the plane, he said, "There will be some significant special attention given to this and what we have learned from it."

(Reporting by Alwyn Scott, Andrea Shalal-Esa and Tim Hepher,; Additional reporting by Karen Jacobs in Atlanta and Kentaro Sugiyama and Yoko Kubota in Tokyo; Editing by Gerald E. McCormick, Steve Orlofsky and Eric Walsh)