Arslan was quoted by state-run news agency Anadolu as saying the ban would be lifted on July 5 following a visit by a US delegation.
Its removal would come after Turkey began using highly sophisticated tomography devices for X-ray and ultrasound at Istanbul's Ataturk International Airport, he said.
US officials are to inspect the machines on Wednesday.
"With this confirmation mission, the ban will be lifted from Ataturk airport and from Turkish Airlines," Arslan said.
Also Read
Late Monday, Turkish Airlines chief executive Bilal Eksi said on Twitter he expected the ban to be lifted on Wednesday.
Arslan was quoted by NTV television as saying Turkey had also been talking with Britain about removing its ban on the transport of laptops in cabin baggage from Istanbul.
Britain imposed the ban on laptops on direct flights originating from Egypt, Jordan, Lebanon, Saudi Arabia, Tunisia and Turkey.
Flag-carrier Turkish Airlines, which has seen exponential international growth in recent years, had responded to the ban by offering laptops to business-class travellers in May.
The decision came after the airline implemented enhanced security measures, a spokesman for the US Department of Homeland Security said.
The ban was put into place after intelligence officials learned of efforts by Islamic State jihadists to produce a bomb that could be secreted inside such devices.
Disclaimer: No Business Standard Journalist was involved in creation of this content