President Trump announced in May that his government was exiting the 2015 accord and would reimpose economic sanctions on the Islamic Republic.
Mr Hook said that the first part of USA sanctions against Iran will snap back on August 6.
The statement said the kingdom will coordinate with other producers.
Last month President Donald Trump withdrew the United States from the 2015 landmark Iran nuclear deal, re-imposing USA sanctions that had been suspended in return for curbs on Tehran's nuclear programme.
International Olympic Committee added 16 new grades of crude during 2017-18 and has the ability to process 175 different varieties, boosting flexibility in oil sourcing.
Trump's comments on Sunday mark an escalation of his already controversial trade policies toward the United States' European allies. Rapidly growing US oil production likely changed the thought process of OPEC ministers, making the decision to raise production easier.
The growing importance of US oil production is likely changing how OPEC producers think about responding to rising prices.
"And so, we are not looking to grant licenses or waivers broadly on the reimposition of sanctions, because we believe pressure is critical to achieve our national security objectives", he said.
The State Department said Monday the USA remained determined to cut Iran's oil exports to zero, despite resistance from importing countries.
"Our focus is on getting as many countries importing Iranian crude down to zero as soon as possible".
Washington aims to cut Iran's oil sales, First Vice President Es'haq Jahangiri said, adding that this is an impossible measure.
"Depending on your belief you could just as easily bet on $100 as $60 by the end of the year", he said in a research note published Monday.
King Salman briefed the cabinet on the telephone call he had received from President Donald Trump during which the two leaders confirmed the need to exert efforts to maintain the stability of oil markets and the growth of the world economy. This reality argues for increasing production in times of tight markets-selling oil now and maintaining market share is likely to be a better strategy than saving it for later when it may be worth less.
"An issue that compels me to write to Your Excellency is that we have not arrived at any decision to assign any allocated production level of any member to others", he said.