US President Joe Biden and Iraqi Prime Minister Mustafa al-Kadhemi spoke about this week's rocket strikes on the US embassy in Baghdad, the White House said Tuesday, with both leaders saying those responsible should be "held fully to account."

The conversation came just days after Biden marked one month in office.

"The President affirmed US support for Iraq’s sovereignty and independence and commended the Prime Minister’s leadership," the White House statement said. 

On Monday, at least three rockets targeted the US embassy in the high-security Green Zone of Iraq's capital Baghdad, in an attack the United States blames on Iran. 

"(Biden and al-Kadhemi) discussed the recent rocket attacks against Iraqi and Coalition personnel and agreed that those responsible for such attacks must be held fully to account," the White House said of the two leaders' call. 

"Together, they discussed the importance of advancing the Strategic Dialogue between our countries and expanding bilateral cooperation on other key issues."

US State Department spokesman Ned Price had said on Monday that the United States holds Iran responsible for the strikes. 

"What we will not do is lash out and risk an escalation that plays into the hands of Iran and contributes to their attempts to further destabilize Iraq," Price told reporters.

The attack was the third in a week to target Western diplomatic, military or commercial installations in Iraq after months of relative calm. 

The attacks are usually claimed by shadowy groups that both Iraqi and US officials say are "smokescreens" for hardline pro-Iran factions inside Iraq. 

Iraq's al-Kadhemi has pledged to put a halt to rocket attacks but struggled to hold the groups to account, infuriating the US.

In October, the US threatened to close its embassy in Baghdad if the attacks did not stop, so hardline groups agreed to an indefinite truce.