The US Department of Homeland Security said it planned to review requests by three Middle Eastern airlines still under a laptop ban to have the restrictions lifted.
The agency will assess airlines from Saudi Arabia, Morocco and Egypt in coming weeks to see if they have introduced security measures to allow the ban to be removed at four airports, DHS spokesman David Lapan said on Tuesday.
Saudi Arabian Airlines, also known as Saudia, said it expected the ban to be lifted on flights from Jeddah and Riyadh by July 19, while Royal Air Maroc believed it could get off the ban for flights out of Casablanca's Mohammed V International Airport by July 19.
State-owned EgyptAir, which has also been covered by the ban, said Tuesday the restrictions would be lifted on Wednesday. Mr Lapan said DHS would confirm the removal of the measures for EgyptAir after they verified the airline's security procedures.
The measures were imposed in March on nine airlines to address the potential threat of hidden explosives in laptops and other devices. The restrictions, coupled with the Trump administration's travel ban on six majority-Muslim countries, hurt the predominantly Middle Eastern carriers.
Over the past 10 days, DHS has lifted restrictions on in-cabin large electronics on six of the airlines after they adopted stricter screening for explosives and other enhanced measures.
They include Royal Jordanian Airways, Kuwait Airways, which saw the ban removed on Sunday. Restrictions on Emirates, Etihad Airways, Qatar Airways and Turkish Airlines were dropped last week.
On June 28, US Homeland Security Secretary John Kelly unveiled enhanced security measures for all foreign flights arriving in the US in what officials said was a move to end a limited in-cabin ban on laptops and prevent its expansion to additional airports.
The new security measures could prompt additional screening time for the 325,000 airline passengers arriving in the US daily.
European and US officials told Reuters airlines had 21 days to put in place increased explosive trace detection screening and 120 days to comply with other security measures, including enhanced screening of airline passengers.
Mr Lapan on Tuesday declined to discuss the timetable for enhanced security procedures, but emphasized that the US government would work with airlines.
"Some airports, airlines will be able to get there more quickly," he said.
DHS is "looking for progress", he added. The US could still impose penalties on airlines that are not moving fast enough, he said.