"We have enhanced our force posture in the region and I am here to deepen our cooperation with our allies to restore deterrence against Iran's attacks, to isolate Iran diplomatically and to build support for our efforts to reverse Iran's power projection", Mr Hook said.
Iran has denied responsibility for those attacks.
Worries about a confrontation between Iran and the United States have mounted despite Trump saying he has no appetite to go to war with Iran.
The drone incident immediately heightened the crisis already gripping the wider region, which is rooted in Trump withdrawing the US a year ago from Iran's 2015 nuclear deal and imposing crippling new sanctions on Tehran.
Speaking in Washington on Saturday before heading to the USA presidential retreat at Camp David, Trump indicated the government was taking a diplomatic path to put pressure on Tehran by moving to impose new sanctions.More news: Oil prices are up, and could go even higher
Around 30 officials from Iran's Islamic Revolutionary Guard Corps and their guests gathered Thursday night in a villa in Tehran to celebrate the downing of a USA drone.
But Trump left that agreement more than a year ago and has imposed a robust slate of punitive economic sanctions created to choke off Iranian oil sales and cripple its economy - one he now plans to expand.
Trump called off the airstrikes not out of any concern for Iranian lives, but rather because his military advisers warned him that that number of deaths in Iran would inevitably lead to retaliation that could claim the lives of even more USA troops, setting off a spiral of military escalation, culminating in a full-scale war that would make the United States interventions in Iraq and Afghanistan look like child's play by comparison.
US President Donald Trump said that he is comfortable with his decision to call off US military strikes, adding that he is "not a warmonger".
The US withdrew from the nuclear deal on May 8 this year, but despite this Iran has remained committed to the deal and to the other agreements within it, according to the International Atomic Energy Agency (IAEA), which inspects Iran's nuclear sites and issues quarterly reports on its compliance. "But they're never gonna do it if they think in five or six years, they're gonna have a nuclear weapon". Trump declared Thursday that "Iran made a very big mistake" in shooting down a USA drone. "They're going on slowly and in some cases pretty rapidly".
Both Trump and Netanyahu call that agreement a mistake and say Obama gave Iran a sweetheart deal.More news: Iran foreign minister tweets map with detailed coordinates of drone
Tensions between the USA and Iran have risen and fallen since the mid-20th century, with the two countries having shared a close relationship at one point.
"A special blessing for the commander who ordered the attack on the American drone and for the fighters who carried it out", said a preacher, according to a guest who spoke with The New York Times.
In this image released by the US Air Force, a RQ-4 Global Hawk unmanned surveillance drone sits in a hangar on February 17, 2019, at Al Dhafra Air Base, United Arab Emirates.
Tensions between the U.S. and Iran have increased in recent weeks amid claims by Washington that Tehran has been behind attacks on oil tankers the Persian Gulf.
"We are putting additional sanctions on Iran", Trump said.
"If the leadership of Iran behaves badly, then it s going to be a very, very bad day for them", he said.More news: YouTube is testing hiding comments in its Android app
His comments followed Trump's assertion that the drone may have been shot down "unintentionally" by Iran.