"Saudi Arabia's approach is to create tension intended to negatively affect the Syrian crisis," Zarif said in a foreign ministry statement.
"We will not allow Saudi actions to have a negative impact," he said.
The statement coincided with a visit to Tehran for talks by Staffan de Mistura, the UN peace envoy on Syria, one week after Saudi Arabia cut diplomatic ties with Iran in a row that began with the Sunni kingdom's execution of a Shiite cleric.
Saudi Arabia and Iran joined world powers at those discussions but there are concerns their split over the execution of cleric and activist Nimr al-Nimr could damage the talks.
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Saudi Arabia's embassy in Tehran and its mission in Mashhad, Iran's second city, were attacked by mobs and set on fire after the killing. Diplomatic ties were cut 24 hours later.
Since then Saudi Arabia has "intensified its actions" against Iran, Zarif said, citing an alleged Saudi air strike said to have caused damage at Iran's embassy in Yemen's capital Sanaa.
"They hide their negative approach by attacking the Islamic Republic of Iran's embassy in Sanaa and injuring the personnel of the embassy," Zarif said.