Aviation authorities in the kingdom, Bahrain and the UAE say the flight ban is to protect its citizens from any threats.
Qatar Airways has said that it is largely unaffected by the decision of several Arab countries to ban the Doha-based carrier from using their airspace.
The Qatari carrier released a statement on Wednesday saying it had operated about 1,200 flights in the past week, 90 percent of which took off within 15 minutes of their scheduled departure times.
“Qatar Airways’ global operations continue to run smoothly, with the vast majority of our network unaffected by the current circumstances,” Akbar Al-Baker, the airline’s chief executive, said in the statement.
Al-Baker also repeated calls for the United Nations’ aviation agency to intervene in the airspace rights dispute.
“We call upon the International Civil Aviation Organisation to declare this an illegal act,” al-Baker said.
“We are not a political body, we are an airline, and this blockade has stripped us of the rights which are guaranteed to us.”
Saudi Arabia, the United Arab Emirates, Bahrain and Egypt are among several countries that suspended ties with Qatar last week, including the suspension of all flights to and from Doha and an airspace ban on Qatar Airways.
State-owned Qatar Airways and other Qatari-owned aircraft are blocked from flying into Saudi Arabia, Egypt, the UAE and Bahrain and from using the airspace over the four Arab countries.
On Tuesday, the four Arab countries said the air embargo applies only to airlines from Qatar or registered there.
Al-Baker said on Tuesday Qatar Airways would redeploy aircraft it used to fly to Saudi Arabia, the UAE, Bahrain and Egypt to fast-track its expansion plans.
The company also said it will continue with plans to add 24 destinations between 2017 and 2018, including two in the next month, despite the restrictions that have forced the airline to fly longer routes to avoid the blocked airspace.
“As far as we are concerned, it is business as usual,” al-Baker said.
Earlier this week, Qatar Airways announced profits of $540m in the fiscal year which ended in March.
Qatar Airways flies to more than 150 global destinations from its Doha hub.