The new closing date is 3 July.
Bids for the contract were originally expected to be submitted on 1 June.
The tender is open to foreign joint stock companies and all international air cargo handling companies.
The appointment of a second air cargo operator at the kingdoms busiest airport is in line with the broad plan to privatise the kingdoms airport services and improve the airports operational efficiency.
Future plans for the Riyadh airport include the construction of a cargo village that will provide world class logistics services.
The airport processed 354,335 tonnes of cargo in 2016, an increase of 8 per cent over the previous year. It processed 23.7 million passengers in 2016, up from 22.5 million in the previous year.
Terminals 1 and 2 at the Riyadh airport cater to international flights, while Terminal 3 caters to domestic flights. Terminal 4 is unused and Terminal 5 was completed in 2015 and began operating in 2016.
The Dublin Airport Authority (DAA) operates and manages Terminal 5. The rest of the terminals are being operated by the Riyadh Airport Company (RAC), a subsidiary of Gaca.
The contract for the renovation works at the old terminals of the airport has been awarded to a team of Turkeys IC Ictas and local Al-Rashid Trading & Contracting in April, following the cancellation last year of an earlier contract awarded to a team led by Germanys Hochtief.
A sixth terminal is to be developed using a public-private partnership (PPP) model once the redevelopment work on the first four terminals has progressed.