The White House said earlier Washington did not want conflict to spread in the Middle East and the US had told Iran it was not involved in an air strike against a top Iranian military commander in Damascus which Iran blames on Israel.
The White House added it warned Iran to not use that attack as a pretext to escalate further in the region.
Iran has vowed to retaliate for the strike in Damascus. Iran's Supreme Leader, Ayatollah Ali Khamenei, said on Wednesday that Israel made a mistake by attacking the Iranian consulate in Damascus and killing the general.
"Israel must be punished and they will pay for their mistakes," he said.
Earlier on Thursday, Iranian sources told Reuters that Iran has signalled to Washington that it will respond to the attack attributed to Israel on its Syrian embassy in a way that aims to avoid major escalation and it will not act hastily.
Iran's message to Washington was conveyed by Iranian Foreign Minister Hossein Amir-Abdollahian 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.
Also on Thursday, Minister of Defense Yoav Gallant spoke with US Secretary of Defense Lloyd Austin.
The Minister and Secretary discussed readiness for an Iranian attack against the State of Israel, which could lead to regional escalation. Minister Gallant detailed preparations, and emphasized that the State of Israel will not tolerate an Iranian attack on its territory.
The Minister of Defense reflected his commitment to the security of Israel’s citizens, as such, a direct Iranian attack on Israeli territory would require an appropriate Israeli response against Iran.