Boeing’s beleaguered 787 Dreamliners will soon be able to resume flights. According to estimates, the grounding has cost Boeing $600 million. (Elaine Thompson/ASSOCIATED PRESS)

Boeing’s revolutionary 787 airliner moved significantly closer to returning to service on Friday when the Federal Aviation Administration approved design modifications for a malfunctioning battery system that caused a worldwide grounding of the new planes.

“These changes to the 787 battery will ensure the safety of the aircraft and its passengers,” Transportation Secretary Ray LaHood said.

Boeing’s stock bumped up nearly 2 percent Friday on reports that the 787 Dreamliner could be cleared to resume service within days. According to estimates, the grounding has cost Boeing $600 million. Officials at several airlines that recently had received 787s or were waiting for them have said they may seek to recover their losses from Boeing.

The FAA ordered that new venting and containment systems be installed to the main and auxiliary battery systems.

“A team of FAA certification specialists observed rigorous tests we required Boeing to perform and devoted weeks to reviewing detailed analysis of the design changes to reach this decision,” FAA Administrator Michael Huerta said.

The FAA added that it would monitor the fixes.

“Any return to service of the modified 787 will only take place after the FAA accepts the work,” the agency said in a statement. “As the certifying authority, the FAA will continue to support other authorities around the world as they finalize their own acceptance procedures.”

In January, the FAA grounded six new Boeing 787 Dreamliners flown by United Airlines after a spate of incidents raised doubts about the safety of the high-tech plane. Aviation agencies in other countries quickly followed suit.

The concern focused on the plane’s lithium batteries, which overheated in two 787s. In one case, alarms went off and the pilots smelled a burning battery on a domestic All Nippon Airways bound for Tokyo.

ANA and Japan Airlines, which fly 24 of the 50 Dreamliners in service, grounded their 787s after the plane made an emergency landing. United is the only U.S. carrier flying 787s.

The FAA said the two battery failures resulted in the release of flammable electrolytes, heat damage and smoke.

In Tokyo, Japan’s transport minister, Akihiro Ota, said Friday that his agency’s review of the 787 problem was near completion, but he said it was unclear how quickly the plane could resume passenger service.

In the United States, the National Transportation Safety Board’s investigation is continuing.

The Dreamliner is the first in a generation of lighter, more fuel-efficient carbon-fiber airplanes in which electronics have replaced hydraulic control systems.

The planes are priced between $207 million and $243 million, and Boeing says more than 800 of them are on order. Boeing is the world’s largest aerospace company and a top U.S. exporter.