Iranian Foreign Minister Mohammad Javad Zarif, speaking by phone with his British counterpart Boris Johnson, said "the allegations by Saudi officials were contrary to reality and dangerous", a foreign ministry spokesman said.
Zarif also slammed "provocative actions by the Saudi government in the region", spokesman Bahram Ghassemi added.
Huthi rebels in Yemen, the targets of a two-year Saudi- led bombing campaign, fired a missile Saturday that was intercepted and destroyed near Riyadh international airport.
"The involvement of Iran in supplying missiles to the Huthis is a direct military aggression by the Iranian regime," the official Saudi Press Agency quoted Crown Prince Mohammed bin Salman as saying.
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This "could be considered an act of war," he said.
Riyadh has accused Tehran of supplying the Shiite rebel group with arms, but a senior Iranian official on Monday rejected such accusations.
"It is very childish to say that Iran has sent missiles to Yemen," the official said, requesting anonymity.
"The Saudis and their supporters know that this is a faked story," he said.
Since Saturday's missile attack, the Saudi-led coalition has tightened its blockade of rebel-held areas of Yemen, blocking even United Nations-supervised relief supplies despite urgent appeals from the world body.
"The best thing to do for Saudis is not try to fish in troubled waters, just to be honest and say that ok, it's time to end the conflict" in Yemen, the Iranian official said.
He added that Tehran would support "any genuine dialogue" between Yemenis.
More than 8,650 people have been killed in Yemen since the start of the intervention.
Repeated attempts to bring about a negotiated settlement to the conflict have failed, including a series of UN-backed peace talks.