He said Tehran's ballistic missile tests and Hezbollah's tunnels are all connected.
Hook told reporters that the United Nations Security Council has been "consistent" for the past 12 years in telling Iran to stop testing and proliferating ballistic missiles and that Iran has been "defying the Council".
He has reimposed sanctions on Tehran and criticized the deal for not including curbs on Iran's development of ballistic missiles or its support for proxies in Syria, Yemen, Lebanon and Iraq.
"Iran's recent ballistic missile test was unsafe and concerning, but not surprising", US Ambassador Nikki Haley said in a statement.
He said that "Russia hasn't embraced Western values of freedom and worldwide cooperation" and added that "Iran has blatantly disregarded U.N. Security Council resolutions".
It requires Iran "not to undertake any activity related to ballistic missiles created to be capable of delivering nuclear weapons, including launches using such ballistic missile technology" until 2024 at the earliest.
He added that Iran has no plans to develop a missile that can carry a nuclear warhead.
British Ambassador Karen Pierce told reporters that the missile test is "inconsistent" with the resolution, but the United Kingdom wants to know "exactly what happened and then we will reach a judgment about how we want to characterize it". Hook asked. "In fact, Iran's security concerns are entirely self generated".More news: Magic Johnson reportedly led free agent pitch for Bryce Harper
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Iran's test of a ballistic missile this month alarmed the West and France called it a destabilising act, but the European Union is focused on protecting the 2015 worldwide nuclear deal with Iran that US President Donald Trump pulled out of in May.
While the U.S. has withdrawn from the nuclear deal, Europe - including the United Kingdom and France - have remained committed to keeping the agreement alive.
The remarks from Paris and London will be seen by the United States government as the first sign that its key European partners may yet be persuaded to view Iran's broader behaviour as so risky that their support for the 2015 Iran nuclear deal can no longer be justified.
The statement came shortly after Security Council met behind closed-doors to discuss Iran's latest alleged missile test, which the U.S. and its allies said may have been in violation of Resolution 2231.
The letter stated that while Britain, France and Germany took "note of Iran's official position on these missile strikes as a response to a terrorist attack in Iran, we assess that Iran's firing of the short range ballistic missiles was inconsistent" with resolution 2231. "No UN Security Council resolution has banned Iran's missile program or missile tests", Qassemi said.
"It is a grave and escalating threat, and nations around the world-not just Europe-need to do everything they can to be targeting Iran's missile program", he added.
Get breaking news alerts and special reports. "This is the most important thing that we must do and the government is putting forth all its efforts on this issue".