His comments came after the US Treasury Department on Wednesday imposed sanctions on two Iranian defense officials, an Iranian company and members of a China-based network for what it called supporting Iran's ballistic missile program. "Iran continues to pursue missile-related technologies capable of delivering a nuclear weapon", Jones said.
Trump administration officials say the White House is carrying out a comprehensive review of USA policy on Iran, which is focused on what officials consider Tehran's expanding influence in the region.
Under the nuclear deal, the USA can continue sanctioning Iran for other, non-nuclear behaviour, although Tehran has threatened to pull out of the deal if the United States and other countries do so.
The dual actions, announced by the Departments of State and Treasury, appeared meant to signal a tough stance on Iran even as Trump continued predecessor President Barack Obama's pact under which Iran agreed to limit its nuclear programme in return for sanctions relief.
The announcements and the report comes just days before Iran holds presidential elections that pit President Hassan Rouhani against several conservative opponents.
Donald Trump's White House has renewed sanctions relief for Iran, despite the U.S. president's past criticism.
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Mr Trump had threatened to tear up the nuclear deal during his campaign and has launched a review of its terms, but until then the deal requires him to renew sanctions relief at regular intervals.
US Secretary of State Rex Tillerson said in April that Iran was complying with its side of the bargain, but he also described the country as the world's leading state sponsor of terrorism. While Rouhani will be able to point to the Trump administration's granting of continued sanctions relief as a victory of the nuclear deal that was achieved on his watch, such grandstanding may have lost the effect that it once had.
However, taking something of a carrot and stick approach, it simultaneously imposed new measures aimed at punishing Tehran for its ballistic missile development programme, human rights record and support for the regime of Syrian President Bashar al-Assad.
The nuclear agreement eased crippling economic sanctions on Iran in return for imposing strict limits on its nuclear program. "Above all, the United States will never allow the regime in Iran to acquire a nuclear weapon".
Iran denies seeking nuclear weapons and its foreign ministry on Thursday condemned the new USA sanctions and announced plans to impose its own against "nine United States individuals and companies".
The new sanctions announced Wednesday hit Morteza Farasatpour, a top Iranian defense official who oversaw the sale of explosives and other materials used by Syria's Scientific Studies and Research Center, the Treasury Department said. "And they were also at the table and they still support the deal".