President Joe Biden said Iran cannot act with impunity and warned it should "be careful", when asked what message he was sending the country with the US air strikes in Syria.
"You can't act with impunity. Be careful," Mr Biden told reporters while travelling to survey the damage from a severe winter storm in Texas.
Mr Biden authorised air strikes against facilities belonging to Iranian-backed militia in eastern Syria on Thursday, in response to rocket attacks against sites in Iraq where the US has a presence as part of the international coalition against ISIS.
France said it stood by the US strikes in view of attacks carried out by Iran-linked Iraqi militias in northern Iraq, which killed a US contractor at a military base near Erbil International Airport on February 15.
"In light of these unacceptable attacks, which we have firmly condemned, we stand with our American allies," the French foreign ministry said on Friday.
The US air strikes targeted militia sites on the Syrian side of the Iraqi-Syrian frontier at Al Bukamal, where groups backed by Iran control an important crossing for weapons, personnel and goods. The crossing has become a staging area for Iranian operations in Syria, with the ultimate goal of launching ballistic missile attacks into Israel, over the Golan Heights. In recent years, the site has been targeted by Israeli air strikes.
Syria may have been chosen as the location of the US air strikes to make the point that Iraq is not an appropriate venue for violent US-Iranian competition. The Iraqi government is ostensibly allied to the US and is host to several joint Iraqi-US bases. There is however strong opposition to the US presence from political parties linked to Iran in Iraq's parliament, and there have been tensions between the conventional Iraqi military and militia groups backed by Iran.
"President Biden will act to protect American and Coalition personnel. At the same time, we have acted in a deliberate manner that aims to de-escalate the overall situation in both eastern Syria and Iraq,” said Pentagon spokesman John Kirby.
The air strikes have nonetheless caused political controversy in Iraq, due to the targeting of Iraqi militias.
The Iraqi military said on Friday that it had not exchanged information with the US regarding targeting locations inside Syria. The denial followed a statement by US Secretary of Defence Lloyd Austin, who said that the Iraqis had provided intelligence that was "very helpful to us in refining the target."
In a possible attempt to reduce political pressure on Iraqi Prime Minister Mustafa Al Kadhimi, Mr Kirby countered Mr Austin's remarks and released a new statement on Friday evening, saying that the US "had not used Iraqi information to develop our targets for last night's strikes".
Mr Al Kadhimi, who was formerly the director of the Iraqi National Intelligence Service, has been accused by Iran-linked groups of passing information to US forces to aid air strikes, including the drone strike which killed the de facto head of Iran-backed forces in Iraq, Abu Mahdi Al Muhandis and Iranian general Qassem Suleimani in Baghdad on January 3 last year.
In a separate attempt to sidestep political controversy, the Iraqi military said that Iraq's co-operation with the US-led coalition was limited to fighting ISIS, a point later echoed by Mr Kirby.