Boeing Co is making progress toward getting its 737 MAX aircraft in the air again but the US Federal Aviation Administration (FAA) will need at least several more weeks for review, FAA Administrator Steve Dickson said on Tuesday.

Dickson said at a conference of air traffic controllers in Washington that the agency had received the ‘final software load’ and ‘complete system description’ of revisions to the plane, which was grounded in March after two fatal crashes.

The disasters, which killed a total of 346 people, and grounding of Boeing's top-selling plane sparked a plunge in the company's share price and disrupted operations at some of the world's biggest airlines, prompting a huge effort by the planemaker to try to get the 737 MAX back into the skies.

But hopes of a quick return to service have slipped to become a more than seven month grounding.

The FAA is currently using ‘aircraft production software’ in the engineering simulator. The next step is to complete pilot workload management testing and have US and international pilots conduct scenarios to determine training requirements before a key certification test flight.

‘It is going to be several more weeks before we go through all of that part of the process,’ Dickson said. ‘We've got considerable work to do.’

Separately, Boeing said that last week it successfully conducted a dry-run of a certification flight test. Dickson told Reuters last month that the FAA would need about 30 days from the time of the certification test flight before the plane could resume flights.

The system description is a ‘500-ish page document that has the architecture of the flight control system and the changes that they have made,’ Dickson told Reuters last month.

Boeing shares rose on Tuesday after two sharp days of declines following the release of instant messages on Friday from a former Boeing pilot that the company had withheld from the FAA and which raised questions about what Boeing may have known about a key safety system.

That prompted an immediate demand for an explanation from the FAA about why the messages were not turned over sooner.

Boeing said on Tuesday it had ‘made significant progress over the past several months’ in its work to return the MAX to service.

Dickson said once the steps were completed ahead of the certification test flight ‘it is a fairly straightforward process to unground the airplane.’ He reiterated he would not let the 737 MAX fly again ‘until I am satisfied it is safest thing out there.’