Boeing on Monday said it expects to resume deliveries of its grounded 737 Max planes as early as next month and that airlines could be able to restart commercial service in January, setting off the biggest rally in the company's shares since June.

Boeing's 737 Max planes have been grounded since mid-March after two fatal crashes killed 346 people.

Investors cheered the new timeline, which indicated the company is near the tail end of the process of winning regulators' approval for Boeing's bestselling planes, even though it was later than the company's previous estimates and repeated delays have prompted airlines to remove the planes from their schedules several times.

Southwest Airlines and American Airlines on Friday pulled the planes from their schedules until early March, nearly a year since regulators' grounding orders.

If the grounding is lifted in December and training approved in January "airlines could resume commercial service," a Boeing spokesman said. "We know they need more time to get their fleets ready and pilots trained, but the plane and training [approvals] will both be done by January, permitting commercial service."

Boeing shares on Monday jumped 4.6%, their largest percentage gain since June 18, to close at $366.96, adding 108 points to the Dow Jones Industrial Average.

The company halted deliveries of the planes after the global ban earlier this year and slashed production by 20% to 42 a month.

Boeing has scrambled to gain regulators' approval for software fixes it has developed for the jetliners after a flight-control program was implicated in both crashes — one in Indonesia in October 2018 and another in Ethiopia in March. Pilots in both crashes were battling the system, known as MCAS, which was activated due to erroneous data from a single sensor.

Boeing has changed the system to include data from two sensors. Lawmakers slammed Boeing CEO Dennis Muilenburg in two hearings on Capitol Hill late last month over the plane's design. Muilenburg admitted the company made mistakes.

The Federal Aviation Administration on Monday reiterated that its officials "have set no timeframe for when the work will be completed."

"The FAA is following a thorough process for returning the Boeing 737 Max to passenger service," the agency said in a statement. "We continue to work with other international aviation safety regulators to review the proposed changes to the aircraft."

The company has completed a test of the software with the FAA in a simulator, one of five tasks required to return the plane to service, the company said in an update Monday.

Boeing also has to to bring airline pilots into 737 Max simulators to assess how cockpit alerts and other factors affect pilot workload. The National Transportation Safety Board criticized Boeing in a report in September for underestimating the impact of such alerts on pilot performance.

Boeing needs to conduct a certification flight with officials and regulators also still have to sign off on new pilot training, which the company expects to have in January.

The grounding has crimped the growth of 737 Max airline customers and cost them hundreds of millions of dollars in revenue after they were forced to cancel flights.

Even after the planes are fully cleared to fly, airlines will have to train thousands of their 737 pilots before they can operate commercially. That process can take more than a month.

Airline executives have said they expect Boeing to pay them for the impact of the grounding. In July, Boeing said it took a $4.9 billion charge to compensate airlines but the final sums have not yet been determined.