Scoop: Iran warns U.S. to stay out of fight with Israel or face attack on troops

• The Iranian supreme leader has threatened "punishment" for Israel but through private channels Iran has signaled it would be limited.
• Israel and the U.S. think an Iranian attack would include the launch of ballistic missiles, cruise missiles and attack drones from Iran to Israeli territory. 
• U.S. officials say the Biden administration asked Israel to notify the U.S. and for the U.S. to have a say before decisions are made about any retaliation by Israel.

The latest: A U.S. defense official told Axios the U.S. is moving additional assets to the region to bolster regional deterrence efforts and increase force protection for U.S. forces.

Behind the scenes: Three U.S. officials said that in recent days the Iranians told several Arab governments they see the U.S. as responsible for the Israeli attack that killed the Iranian general in Damascus, regardless of U.S. efforts to distance itself from the strike.

• The U.S. maintains it had no involvement in the strike, a senior U.S. official said.
• The Iranian message was that if the U.S. gets involved after an Iranian attack on Israel, U.S. bases in the region will be attacked.
• "The Iranian message was we will attack the forces that attack us, so don't f--k with us and we won't f--k with you," one U.S. official said.

Between the lines: President Biden and other U.S. officials have said publicly the U.S. would help Israel defend itself against Iranian attacks.

• Secretary of Defense Lloyd Austin told Israeli Minister of Defense Yoav Gallant in a call on Thursday that Israel "could count on full U.S. support to defend Israel against Iranian attacks, which Tehran has publicly threatened," the Pentagon said.
• Gallant told Austin "a direct Iranian attack will require an appropriate Israeli response against Iran."
• A U.S. official told Axios it wasn't clear from the message received via several Arab countries whether the Iranians were threatening to attack U.S. forces if they help Israel intercept Iranian missiles or only if they participate in an Israeli retaliation.
• The general assessment of the U.S. intelligence community is the Iranians could attack U.S. forces only if the U.S. joins Israel in a counteroffensive, according to the U.S. official.

Yes, but: Iran is sending a different message through other communication channels, including calls between the foreign ministers of the UK, Australia and Germany and their Iranian counterpart on Thursday.

• Two U.S. officials said the Iranian message in these calls was more nuanced and signaled the Iranians are aimed at a limited response that will not lead to a regional escalation.
• Another U.S. official said the U.S. is communicating directly with Iran through the formal Swiss channel of communication and Iran did not communicate threats through this channel.
• U.S. officials have been in touch with regional partners to discuss efforts to message to Iran to not escalate the situation, a U.S. official said.
• They've also been in touch with Israel to ensure they are able to defend themselves and at the same time prevent tensions from escalating, the official added.

What to watch: U.S. CENTCOM commander Gen. Michael "Erik" Kurilla is in Israel to coordinate the U.S.-Israeli defensive effort ahead of any possible Iranian strike, U.S. and Israeli officials said.

• The officials stressed the Biden administration asked Israel in recent days to notify and consult the U.S. in advance of any Israeli retaliation against Iran.   
• The Biden administration felt Israel didn't consult and didn't give it an appropriate notice before its strike in Damascus that killed the Iranian general, even though such a strike could have had implications for U.S. forces in the region.
• The Washington Post reported Austin complained to Gallant in a call on April 3 about the lack of sufficient notice from the Israeli side.

Editor's note: This story was updated with additional comments.