"We consider the security of Yemen to be the security of the region and of Iran. Others will not be allowed to play around with our common security with their adventurist actions," the site quoted him as saying.
"The fact that Saudi Arabia is focused on the war against Yemen only benefits the Zionist regime and terrorist groups," said Amir-Abdollahian.
Iran refers to Israel using the term "Zionist regime".
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He also said Tehran supported "an inter-Yemeni dialogue at a venue agreed on by all (Yemeni) parties with no foreign interference".
Saudi Arabia and its Arab coalition allies, waging a campaign of daily air strikes against Shiite Huthi rebels and their allies in Yemen, want any talks on a settlement to be held in Riyadh, rejecting Tehran's calls for international talks outside the Saudi orbit.
Shiite Iran backs the Huthis, and denounces the campaign of air strikes by Sunni states.
Tehran has always denied giving the Huthis logistical support, but according to a confidential UN report, Iran began arming in 2009 early on in the Shiite uprising in north Yemen.
Tensions between Riyadh and Tehran have been rising steadily, not only over Yemen but also on the situation in Syria, Iraq, Lebanon and Shiite-majority but Sunni-ruled Bahrain.