Iran has signaled to Washington that it will respond to Israel's attack on its Syrian embassy in a way that aims to avoid major escalation and it will not act hastily, as Tehran presses demands including a Gaza truce, Iranian sources said, Ednews informs via Reuters.

Iran's message to Washington was conveyed by Iranian Foreign Minister Hossein Amirabdollahian during a visit on Sunday to the Gulf Arab state of Oman, which has often acted as an intermediary between Tehran and Washington, the sources said.

A White House spokesperson declined to comment on any messages from Iran but said the United States has communicated to Iran that it was not involved in the strike on the embassy.

Iran's foreign ministry was not immediately available to comment. The Omani government did not immediately respond to emailed questions for comment, sent during the Muslim Eid al-Fitr holiday.

A source familiar with U.S. intelligence was not aware of the message conveyed via Oman but said Iran has “been very clear” that its response to the attack on its Damascus embassy compound would be “controlled” and “non-escalatory” and planned “to use regional proxies to launch a number of attacks on Israel.”

The diplomatic messaging points to a cautious approach by Iran as it weighs how to respond to the April 1 attack in a way that deters Israel from further such actions, but avoids a military escalation that could suck in the United States.

Iranian Supreme Leader Ayatollah Ali Khamenei said on Wednesday that Israel "must be punished and it shall be", saying it was tantamount to an attack on Iranian soil. Israel has not confirmed it was responsible, but the Pentagon has said it was.