"We are going to increase our sanctions on Iran and continue our foreign policy," Hook told CNBC's Hadley Gamble in Abu Dhabi on Saturday.
Hook said a lot of pressure is needed in order to address Iran's "regional aggression" and a new foreign policy devised by the U.S. aims to bring Iran back to the negotiating table.
"When the President (Trump) got out of the Iran deal, we put a new foreign policy that does a couple of things. It is going to deny the regime the revenue that it needs to run a violent and expansionist foreign policy. But it is also designed to bring them back to the negotiating table," Hook said.
"So ultimately we would like to have a new deal that addresses Iran's regional aggression, the missile program and its nuclear program. In order to do that, it is going to take pressure. And in order to get Iran to change its behavior, it is going to take a lot of pressure. So we are going to increase our sanctions on Iran, we are going to continue with this foreign policy," he added.
When asked what these sanctions would entail, Hook said the U.S. doesn't "preview sanctions."
"We don't ever preview our sanctions because that's part of our strategy. When we go after assets, we don't want to give them time to hide that or create workarounds," Hook said.
"But I can say that when you look at Iran's largest sources of export revenues - it's oil, petrochemicals, precious metals and industrial metals. We have now sanctioned all four of those categories. We have blacklisted over 70 Iranian banks that the Swift financial system also matched our sanctions. We have collapsed foreign direct investment. We are driving up the cost of the Iranian regime for behaving the way it does."
Hook's comments come after a series of rapid escalations between Washington and Tehran.
President Donald Trump reportedly approved military strikes against the Islamic Republic late Thursday in retaliation for the downing of an unmanned American drone, before abruptly reversing his decision.
The U.S. president has since said in an interview with NBC News that he does not want war with Iran but, if it comes, there will be "obliteration like you've never seen before."
Trump said the U.S. was "cocked and loaded to retaliate" against Iran on Thursday, but he changed his mind 10 minutes before planned strikes.
Attacks had been planned against three sites in response to the downing of a U.S. Global Hawk drone.
U.S. officials said the drone was flying over international waters in the Strait of Hormuz — the world's busiest transit lane for seaborne oil shipments — but Iran claims it entered its airspace.
"It is an outlaw regime, it is corrupt religious mafia that exports violence around the middle east and around the world. And we are standing up to it in ways that has no historic precedent," Hook said.
Correction: Iran said that the U.S. military surveilllance drone had violated its airspace. A previous version of this story misstated Iran's position.