The declaration, by a top security official, comes after the head of the UN nuclear watchdog said a report into the possible military dimensions of Iran's activities would not be "black and white."
Iran has always denied seeking to develop an atomic weapons capability, insisting its nuclear programme is for peaceful energy production and medical purposes only.
Referring to the Joint Comprehensive Plan of Action, the July 14 agreement's official name, Admiral Ali Shamkhani, said anything short of the watchdog's probe being closed was unacceptable to Iran.
Shamkhani is secretary of Iran's Supreme National Security Council (SNSC), the country's highest security body, which was tasked with supervising the nuclear deal.
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The committee reports to supreme leader Ayatollah Ali Khamenei, who has the final word on all policy decisions.
Under the July 14 accord, Iran agreed to major curbs on its atomic programme, particularly its enrichment of uranium to high purities, in return for the lifting of all nuclear-related sanctions imposed by the US, the European Union and the United Nations.
"The P5+1 must choose between the JCPOA and leaving open the so-called PMD file," he said.
The probe concerns allegations, rejected by Iran, that at least until 2003 it conducted research into how to make a nuclear weapon.