Saudi Arabia has been leading an aerial bombing campaign in support of the government and against the Iranian-backed Houthi rebels.
Saudi forces on Sunday intercepted seven missiles fired by the Huthi rebels toward cities in Saudi Arabia, including the capital Riyadh, killing one person.
A USA official said Washington would support Saudi Arabia's "right to defend its borders" following missile attacks on the kingdom from Yemen's Iran-backed Houthi militia.
Iran has repeatedly denied giving missiles to the Houthis.
"If Iran is genuinely committed to supporting a political solution in Yemen - as it has publicly stated - then it should stop sending in weapons which prolong the conflict, fuel regional tensions, and pose threats to global peace and security", they claimed in the joint statement.
The Saudis have maintained the narrative that Iran is behind the Yemen War throughout, but have struggled to prove the weapons smuggling they allege.
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Several Western countries, the United States and the UK in particular, are accused of being complicit in the Saudi-led aggression on Yemen as they supply the Riyadh regime with advanced weapons and military equipment.
Qassemi also rejected the claims on the provision of Yemenis with missiles and said, "By leveling baseless and imaginary accusations without evidence against others, the Saudis are trying to cover up their inability and consecutive defeats they have suffered ... in the war against Yemeni people despite possessing ... a collection of advanced weapons and multi-billion-dollar arms purchases".
The independent watchdog said it examined a fiberglass-encased bomb, packed with explosives, and found a type of Chinese-manufactured wire covering used in other Iranian materiel. "He tried to convince me that Israel should strike Iran".
"They may make similar moves in order to be seen to be doing something, but it won't really change the dynamics of the conflict", said Jane Kinninmont, Middle East expert at Chatham House in London.
Western countries have urged Saudi Arabia and its Gulf Arab allies to protect civilians and find a quick end to Yemen's war.
Iran's ambassador to the United Nations has rejected baseless Saudi allegations of Tehran sending missiles to Yemen, urging the regime in Riyadh to stop "warmongering" and engage, instead, in dialog with its neighbor.