"The Guards' naval force had no exercise in the past week when the Americans claim that a missile or rocket was fired in the Hormuz Strait area," spokesman General Ramezan Sharif said on the Guards' official website.
The Guards naval unit is responsible for securing Iranian interests in the Strait, a vital waterway for a large proportion of the world's oil, regularly patrolling the area and conducting exercises.
A US military official said an Iranian vessel had test- fired several rockets near three Western warships including the USS Harry S Truman aircraft carrier on December 26.
Though the rockets were not fired toward any warship, their proximity to the foreign vessels - and several commercial vessels - was "highly provocative", said the official, who was not authorised to be named.
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Sharif accused the United States of lying about the incident - which reportedly occurred after Iranian naval forces announced via radio that the test-firing was to begin.
"Publishing such lies in the current situation is more a psychological operation," he said.
"The security and peace of the Gulf is of serious strategic importance to Iran. The Guards conduct exercises to increase our required preparedness at due times, based on our own schedule."
While heralded by moderates, such as Iran's President Hassan Rouhani, hardliners in Tehran have criticised the agreement as being against national interests.
Since the deal was struck on July 14 - it has not yet been implemented - Iran has conducted missile tests criticised by the US and also aired footage on state television of an underground missile base.