The Federal Aviation Administration gave formal approval on Thursday for a new lithium-ion battery system for Boeing Co's 787 Dreamliner, ending a three-month ban and clearing airlines to fly the plane with passengers again.

The FAA's "airworthiness directive" technically applies just to United Airlines, which so far is the only U.S. carrier with the new high-tech jet, but it will set the standard that regulators in Japan, Europe and elsewhere will follow. Other U.S. carriers with 787s on order will eventually come under the new rule.

The FAA pegged the cost of repairing United's six jets at about $2.8 million.

The approval caps a tumultuous period for Boeing and its airline customers, beginning when two lithium-ion batteries overheated on two Dreamliners in separate incidents less than two weeks apart in January.

The two planes are owned by Japan Airlines and All Nippon Airways, which together own nearly half the fleet of 50 Dreamliners delivered so far. The ban on flights effectively halted deliveries of new planes to customers.

Boeing devoted thousands of hours to developing a fix, even before investigators determined what caused the batteries to overheat, emit smoke and, in one instance, catch fire. That investigation continues, led by the U.S. National Transportation Safety Board, which held hearings this week on the issue.

Last week, the FAA gave Boeing permission to begin installing the new battery system on planes. On Wednesday, the company said it expected to resume deliveries early next month and finish retrofitting the 50 customer planes by mid-May.

(Reporting by Alwyn Scott; Editing by Gerald E. McCormick and Lisa Von Ahn)