Boeing had said it would present the solution to the FAA last week, and it had gathered hundreds of industry representatives at its facilities in the Seattle area last Wednesday to demonstrate software changes.
But the FAA said Monday that the company concluded "additional work" is needed.
"The FAA expects to receive Boeing's last package of its software improvement over the coming weeks for FAA approval," the agency said in a statement. "Time is needed for further work from Boeing as a result of a continuous review of the 737 MAX Flight Control System to ensure that Boeing has identified and appropriately addressed all relevant issues.
Boeing acknowledged the new timeline and said in a statement that the software change would be "completed in the coming weeks." It didn't say why the timeline had changed.
"Security is our first priority and we will take a thorough and methodical approach to the development and testing of the update to ensure that we take the time to get it right," said the company.
US Airlines said Monday afternoon that it was aware MAX "may be delayed longer" in return for service. It has been forced to cancel dozens of flights daily while the planes are waiting for a solution.
Captain. Dennis Tajer of the Allied Pilots Association, which represents US airlines, said the group was encouraged by Boing's recent "energy settlement" to make a solution, but also realized that the timeline was ambitious.
"We ignored it because we had the pilots fully engaged as they are and all the information, and knowing what the training will be all, putting it off more of a distant timeline to get the plane to fly , "Tajer told CNN.
FAA followed other countries' aviation authorities by grounding MAX on March 13 after the second crash of less than five months. The agency said it had undergone satellite data and physical evidence showing similarities between the Lion Air flight crashing in October and the Ethiopian Airlines flight that crashed days earlier in March.
A preliminary report on the Ethiopian accident is expected in the coming days.
Software designers, Boeing engineers and test pilots had made a set of changes to a stabilization system known as MCAS, which has been under the control of investigators using the Lion Air crash, according to a company official. The solution brings in several layers of protection and is accompanied by a training regime.
Tajer from the Allied Pilot Association said the software changed Boeing demonstrated last week "targeting the concerns we voted for Boeing" after the October incident.
The FAA statement said software changes would require a "rigorous security assessment".
"The FAA will not approve the software for installation until the FAA is satisfied with the submission," said the agency.
CNN's David Shortell contributed to this report.