The US has condemned Iran over ballistic missile attacks near Iraq's northern city of Irbil, calling them "a reckless and imprecise set of strikes".
Iran's Revolutionary Guards said they struck what they claimed were Israeli "spy headquarters" in Iraq's semi-autonomous Kurdistan Region.
Four people were killed and six wounded in Monday's attack, according to the Kurdistan Region Security Council.
Iraq denounced the attacks, calling them a violation of its sovereignty.
Israel's government has not commented on the Iranian claims.
In a separate development, Kurdistan authorities said on Tuesday morning they had shot down three armed drones flying over Irbil airport, where US and international forces are stationed, Reuters reported. Authorities did not provide information on damage or casualties.
The Iranian strikes come amid rising tensions in the region since the war between Israel the Iran-backed Palestinian group Hamas broke out in the Gaza Strip on 7 October.
The conflict has increasingly started to spill over to involve militias allied to Iran operating in Lebanon, Syria, Iraq and Yemen.
"We will continue to assess the situation, but initial indications are that this was a reckless and imprecise set of strikes," Adrienne Watson, spokesperson for the White House National Security Council, said in a statement.
"The United States supports the sovereignty, independence, and territorial integrity of Iraq," she said, adding that no US personnel or facilities were targeted.
Iran's Revolutionary Guards said that "one of the main Mossad espionage headquarters in Iraq's Kurdistan Region was destroyed with ballistic missiles".
A statement said it was "in response to the recent atrocities of the Zionist regime".
Iran has carried out missile attacks in Iraqi Kurdistan before, targeting what it said were sites used by Iranian separatist groups and agents of Israel.
The Prime Minister of the Kurdistan Regional Government, Masrour Barzani, condemned the latest attack on Irbil as a "crime against the Kurdish people".
A prominent businessman, Peshraw Dizayee, was among four civilians killed, Mr Barzani's Kurdistan Democratic Party said.
The Revolutionary Guards also said they had targeted Islamic State (IS) group positions in Syria on Monday night.
Explosions were heard in the north-western city of Aleppo and its countryside, where "at least four missiles that came from the direction of the Mediterranean Sea" fell, the UK-based Syrian Observatory for Human Rights war monitor said.
The Revolutionary Guards said the strikes in Syria were in retaliation for this month's suicide bombing that targeted crowds marking the anniversary of Iranian general Qasem Soleimani's assassination by the US.
That attack in Kerman, in southern Iran, killed at least 94 people and wounded many more.
