Iran has signalled 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.

Iranians attend a rally marking Quds Day and the funeral of members of the Islamic Revolutionary Guard Corps, in Tehran.

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.

The attack, which killed a top Iranian general, marked an escalation in the violence that has spread through the region since the Gaza war began. Tehran has carefully avoided any direct role in the regional spillover, while backing groups which have waged attacks from Iraq, Yemen and Lebanon.

Iranian-backed Shiite Muslim militias have not attacked U.S. troops in Syria and Iraq since early February.

One of the Iranian sources did not rule out the possibility that members of the Iran-backed Axis of Resistance could attack Israel at any moment - an option analysts have flagged as one possible means of reprisal.

The sources said Amirabdollahian, in his Oman meetings, signalled Tehran's willingness to de-escalate on condition demands are met, including a permanent Gaza ceasefire - something Israel has ruled out as it seeks to crush Hamas.

The sources said Iran also sought the revival of talks over its disputed nuclear programme. Those talks have been stalled for nearly two years, with both sides accusing each other of making unreasonable demands.

And Tehran also sought assurances that the United States would not get involved in the event of a "controlled attack" on Israel by Iran - a demand which the United States rejected in a response delivered via Oman, the sources said.

Iran’s retaliatory strikes would be “non-escalatory” toward the United States “as they don’t want the U.S. to get involved,” said the source familiar with U.S. intelligence, indicating Iran would not direct its proxy militias in Syria and Iraq to target U.S. forces in those countries.

U.S. President Joe Biden said on Wednesday that Iran was threatening to launch a "significant attack in Israel", and that he had told Netanyahu "our commitment to Israel security against these threats from Iran and its proxies is iron-clad".

Israel has said it would answer any attack from Iran.

“If Iran attacks from its territory, Israel will respond and attack in Iran,” Israeli Foreign Minister Israel Katz said in a post on the X social media platform in Farsi and Hebrew on Wednesday.

IRAN'S 'CONUNDRUM'

Experts on Iranian diplomacy said such tough demands from Tehran were typical of the hard-nosed approach it takes in negotiations. But the contacts nevertheless pointed to its interest in warding off major conflict.

Eurasia group analyst Gregory Brew said Khamenei was "trapped in a strategic conundrum".

"Iran must respond to restore deterrence and maintain credibility among its Resistance Front allies. But on the other hand, retaliating to restore deterrence would likely bring an even greater, and more destructive Israeli response, likely with U.S. assistance," he said.

The Iranian sources said the U.S. had asked Iran to exercise restraint and allow space for diplomacy, cautioning Tehran that in the event of a direct attack it will stand by Israel.

The Iranian sources said Iran believes Netanyahu aims to draw Tehran into a war, therefore its retaliation could be a restrained one that avoids direct strikes on Israeli territory and may draw on Tehran's allies.

The U.S. Middle East envoy has called the foreign ministers of Saudi Arabia, UAE, Qatar and Iraq to ask them to deliver a message to Iran urging it to lower tensions with Israel, a source with knowledge of the situation said.

A source familiar with the issue said the U.S. might well agree to revived nuclear talks if that could prevent a conflagration.

“If we are talking about talks and not (about) reaching an agreement, then it would seem to be well worth the price if the payoff is minimizing the risk of a regional escalation into which the U.S. would be dragged,” said the source, who spoke on condition of anonymity.

Ali Vaez of International Crisis Group said Iran’s dilemma was "to figure out how to retaliate in a way that it saves face without losing its head".

"Israel is much more unpredictable than the U.S.," he said. "The Supreme Leader is clearly concerned that rather than delivering the deterrent effect he might hope to achieve, an attack on Israel may only fuel a counter-escalation he might have hoped to avoid."