The aircraft has been grounded since March.
FAA representatives had told members of the aviation industry last month that approval of the 737 MAX jets could happen as early as late June.
Emery implores board to sign £130,000-a-week Premier League star
He is now in Egypt for the Africa Cup of Nations where he is due to play in their opening game against South Africa on Monday. Arsenal are also keen on getting homegrown talent into a squad that will lose Aaron Ramsey on a free to Juventus.
Much of the attention since the Lion Air and Ethiopian Airlines crashes has focused on the on the Maneuvering Characteristics Augmentation System (MCAS). In all, 346 people died. "The FAA will lift the aircraft's prohibition order when we deem it is safe to do so".
Reuters, which first reported the new issue, said during an FAA pilot simulation in which the stall-prevention system was activated, it took longer than expected to recover the aircraft.
Boeing says in a statement that the company is working on the required software fix to address the FAA's request.
Exercises on a Boeing 737 Max simulator in recent days showed pilots might have difficulty responding to the newly identified failure, the person said.
Boeing's aircraft are being subjected to intense scrutiny and testing created to catch flaws even after a years-long certification process. Southwest Airlines and American Airlines had already made similar announcements - an acknowledgement that the plane won't return to flying as soon as the airlines had hoped.
Michael B. Jordan pressenti pour jouer Morpheus dans un prochain "Matrix"
Je veux dire, Matrix reste un de mes films préférés... "S'ils le ressortaient aujourd'hui, les gens iraient le voir". Et cela tend à se confirmer, puisque Discussing Film a confirmé que le film aurait pour acteur principal Michael B.
The flaw could result in the plane's nose pitching down, two people familiar with the matter told the Associated Press news agency.
Boeing said addressing the issue "will reduce pilot workload by accounting for a potential source of uncommanded stabilizer motion".
Boeing said it agrees with the FAA's decision and is working to fix the problem.
One said the latest setback is likely to delay the plane's return to service by an extra one to three months.
The US manufacturer on Wednesday confirmed that, during simulator tests on the embattled jetliners, the 737 Max's new control software would lock up a microprocessor resulting in the plane automatically entering a risky nosedive.
Maisie Williams turns to comedy after Game of Thrones
Game Of Thrones star Maisie Williams is to star in a new Sky comedy series about a misfit on the run from a murderous gangster. They add: "With the survival techniques she has picked up from her upbringing, however, she might just get through".