Mr Salman made this known at a news conference on Tuesday.
“Over the past two days, we were able to contain the damage and restore more than half of the production that was disrupted due to the terrorist attack,” he said.
He added that Aramco will fulfill all its commitments towards its clients this month through withdrawing from its stocks of crude oil.
He expected that the production capacity will return to 11 million barrels per day by the end of September and to 12 million barrels by the end of November.
“Not a single shipment to an international customer has been or will be missed or canceled as a result of these attacks,” Aramco’s CEO Amin Nasser told journalists in Jeddah.
Drone attacks at the weekend targeted two facilities operated by Saudi state oil giant Aramco in the eastern province of Buqyaq, forcing the kingdom to halt about half its oil supplies afterwards.
Earlier in the day, Saudi Arabia’s King Salman bin Abdelaziz said that the kingdom is able to deal with the consequences of the “cowardly attacks” that targeted the Saudi oil facilities.
In a cabinet meeting, the king said the attacks not only target the kingdom’s vital facilities, but also the global oil supply and the stability of the world economy.
The “kingdom will defend its lands and vital facilities, and is able to respond to such acts whatever their source is,” said the cabinet.
Oil prices were sent soaring following the attacks, which were claimed by Houthi rebel fighters in Yemen who are backed by Iran.