"We have pretty big confidence we can be done with this in a few weeks, by mid-May," Jim McNerney, Boeing chairman, president and chief executive, said in a conference call after the company reported first-quarter earnings.
Boeing has begun the process of modifying the battery systems internationally, and deliveries of the aircraft were expected to resume in early May, McNerney said.
Boeing had to come up with a fix after two battery incidents led to the global grounding of all 50 Boeing 787s in service in mid-January.
Boeing's proposed modifications for the pioneering lithium-ion battery system to make the plane safer won US Federal Aviation Administration approval last Friday.
The FAA will have to approve the installations on US airlines before allowing the plane to fly again. United Airlines has six 787s, the sole US carrier owning the Dreamliner.
On Tuesday, the European Aviation Safety Agency announced its approval of the Boeing plan.
But separately, the National Transportation Safety Board, which investigates aircraft accidents, said Tuesday that they still are not certain what caused the incidents.
The problems first surfaced publicly when a fire erupted in the battery area of a Japan Air Lines 787 parked at a Boston airport on January 7.
Then on January 16 battery fumes forced an emergency landing of an All Nippon Airways 787 in Japan, prompting the global grounding.
Japan's two biggest airlines operate about half the 787s in service. Japanese regulators said Tuesday that they would make a final decision on allowing the 787 to fly after two-day hearings being held by the NTSB, which were to conclude Wednesday.
Despite the grounding, Boeing expects to deliver more than 60 of the high-tech Dreaminliners this year, a company spokesman said.
It only has delivered one 787 so far this year, to Air India in early January before the grounding.
The aerospace giant continues to produce 787s at a rate of five per month and has maintained its target of 10 per month by year-end.
In the earnings conference call, Boeing chief financial officer Greg Smith declined to estimate the cost of the grounding, but said it would not have a significant impact.
McNerney refused to provide details about any compensation claims from airline customers because of the groundings.
Smith underscored that Boeing would work with customers. "There's a variety of ways to insure the disruption doesn't hurt their results and operations."
He estimated the 787 program would break even, on a per unit basis, "about two years from now."