Qatar Airways has sought to play down the impact of the deteriorating political situation in the Middle East on its operations.
Several Gulf countries cut travel and embassy links with Qatar on Monday, including the United Arab Emirates, Egypt and Saudi Arabia.
Disruption to airspace in the Gulf began almost immediately, with flights into Doha cancelled by Etihad Airways and Emirates, among others.
Saudi Arabia and Bahrain have also revoked the licences of Qatar Airways and ordered its offices to close, while airspace across the region has been closed to flights from Doha.
However, Qatar Airways said flights we operating as “normal”.
The additional flights have been added to carry stranded Qatar Airways passengers from Saudi Arabia to Muscat, the carrier added.
“Qatar Airways operations are running as normal with no disruptions to flights with the exception of those to the four countries Qatar Airways has been restricted to fly to,” explained a statement.
Saudi Arabia, Egypt, Bahrain, the United Arab Emirates and Yemen have all cut ties with Qatar, stating the country backs militant groups including so-called Islamic State and al-Qaeda.
Qatar has denied the accusation.
In response Etihad Airways said it would cancel all flights to and from Doha.
The Abu Dhabi-based carrier currently operates four flights a day to the Qatari capital.
Emirates took a similar decision, cancelling its four daily flights.
flyDubai, the leading budget carrier in the region, said it would also cancel all flights.