Passengers flying direct from Dubai and Turkey to the United States may soon be able to take their laptops on board again.

In March, the U.S. banned electronics devices larger than a smartphone from the cabin on several airlines flying from the Middle East, because it was worried they could be used to smuggle explosives on board.

Last week, the Department for Homeland Security (DHS) lifted the ban for Abu Dhabi's Etihad Airways because it had put additional security measures in place. Emirates and Turkish Airlines are next in line.

"Turkish Airways and Emirates Airline have initiated the process for lifting the ban by alerting the [Transportation Security Administration] they are ready to comply with the enhanced security measures," a DHS spokesman told CNN on Tuesday.

"TSA is scheduled to visit Turkish Airways and Emirates Airline [on July 5] to verify the measures have been implemented correctly and to the full extent required."

Turkish Airlines CEO Bilal Eksi confirmed on Twitter that he expected the ban to be lifted Wednesday.

Emirates, the largest international carrier in the world, said Tuesday that it was in talks with the DHS on new security guidelines.

"We hope that we will receive validation that all measures have been successfully implemented so that the electronics ban can be lifted as soon as possible for our U.S. flights," an Emirates spokesperson said in a statement.

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Assuming that happens, the ban will still apply to U.S.-bound flights from seven other airports in the Middle East and North Africa. It will continue to affect six airlines.

One of them is the national carrier of Saudi Arabia.

Saudia said Tuesday it was working to implement the DHS measures and aims to have the ban lifted by July 19.

"We're not in a position to confirm so far in advance," the DHS spokesman said. "Saudi Arabian Airlines is still operating under the [portable electronic device] restriction."

The new security measures were alluded to last week by DHS Secretary John Kelly, who said they included enhanced screening of passengers and electronic devices.