Hook made the comments on Wednesday in an interview with the Al-Jazeera satellite television network.
He also said the United States may impose fresh sanctions on Iran, according to Twitter posts from Al-Jazeera, Presstv Reported.
Iran has ruled out renegotiating the deal, also known as Joint Comprehensive Plan of Action (JCPOA).
The Trump administration argues that one of the problems of the deal agreed under Trump's predecessor Barack Obama is that it was not formally approved by the US Congress.
Tensions have been running high between the US and Iran since Washington’s decision in May last year to abandon the 2015 Iran nuclear deal and reimpose sanctions on Tehran as part of a “maximum pressure” campaign aimed at forcing it to renegotiate a new deal that addresses its ballistic missile program and regional influence as well.
Tensions between the two nations deteriorated after Iran shot down a US surveillance drone on June 20 following its violation of Iranian airspace, although Washington insists that the aircraft was flying above international waters.
Several oil tankers were also targeted near the Persian Gulf last month, with Washington and its ally Saudi Arabia quickly blaming Iran for the suspicious attacks.
Tehran has rejected the accusations of its involvement as baseless, saying the incidents in the Sea of Oman appear to be false flags meant to frame the Islamic Republic.
The United States has engaged in significant regional military buildup, including by sending an aircraft carrier, a bomber task force, an assault ship, and around 1,500 additional forces to the Middle East.
Tehran has time and again said that it does not seek military confrontations with the United States, yet stands ready to defend its interests in the region.