Jordan summoned Iran's ambassador in Amman on Wednesday to condemn an attack on the embassy of Saudi Arabia in Tehran and "Iranian interference" in Arab affairs, Jordanian state news agency Petra reported.
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Tensions between Iran and Saudi Arabia have spiraled since the execution of a Shi'ite cleric in Saudi Arabia.
Iranian protesters stormed the Saudi embassy in Tehran early on Sunday and Shi'ite Iran's top leader, Ayatollah Ali Khamenei, predicted "divine vengeance" for the execution of Sheikh Nimr al-Nimr, an outspoken opponent of the ruling Al Saud family.
The Jordanian government stressed its condemnation "of the Iranian interference in the internal affairs of Arab states", the Petra news agency said. It also rejected Iranian statements it said represented "interference in internal Saudi affairs".
The Iranian ambassador was told to relay the Jordanian position to his government immediately.
Iraq, meanwhile, offered made an offer to mediate between the two regional rivals to reduce tensions on Wednesday.
The Shi'ite-led government in Baghdad relies on Iranian help to battle the extremist Islamic State group, but is also trying to repair ties to oil-rich Saudi Arabia, which last week sent an ambassador to Baghdad for the first time in 25 years.
Iraqi leaders are also counting on internal unity between Sunnis and Shi'ites to push back ISIS and prevent sectarian reprisals.
Iran has accused the Sunni Muslim monarchy of Saudi Arabia of using the attack on the embassy as an "excuse" to sever ties and further increase sectarian tensions.