After a deadly rocket attack that killed one British and two American troops at a base north of Baghdad, a top U.S. general held Iran-backed militia groups responsible, in remarks that leave the door open to potential escalation with Tehran.

U.S. Marine General Kenneth McKenzie, the head of Central Command, did not blame any specific militia but noted that only Iran-backed Kataib Hezbollah had been known to wage such an attack in the past. Washington blamed that militia for a strike in December that killed a U.S. contractor.

"While we are still investigating the attack, I will note that the Iranian proxy group Kataib Hezbollah is the only group known to have previously conducted an indirect fire attack of this scale against U.S. and coalition forces in Iraq," McKenzie told a U.S. Senate hearing on Thursday.

The Turkish Foreign Ministry on Thursday condemned the deadly rocket attack on an Iraqi military base of the anti-Daesh coalition. Turkey called on the Iraqi authorities to capture the perpetrators of the attack and bring them to justice and urged the authorities to take "necessary measures to prevent such attacks from reoccurring."

The U.N. also condemned the attack, saying it took "critical political attention away" from Iraq's ongoing domestic challenges, which threaten to create a power vacuum at the seat of Iraq's government.

Heightened tensions between the U.S. and Iran in recent months were set in motion by a rocket attack in December on an Iraqi base that killed a U.S. contractor. American airstrikes targeting the Iran-backed militia Kataib Hezbollah followed, which led to protests at the U.S. embassy in Baghdad.

A U.S. drone strike in Baghdad then killed Iranian Gen. Qassem Soleimani, a top commander responsible for expeditionary operations across the wider Mideast. Iran struck back with a ballistic missile attack on U.S. forces in Iraq, the Islamic Republic's most direct assault on America since the 1979 seizing of the U.S. Embassy in Tehran.

Wednesday's attack coincided with what would have been Soleimani's birthday.

The potential power vacuum looming over Iraq comes after the prime minister-designate, Mohammed Allawi, withdrew his nomination earlier this month. That followed political squabbling over the naming of his cabinet. Shortly afterward, the caretaker premier, Abdul-Mahdi, said he would no longer carry out most of his official duties and called for early elections.

There are at least 5,200 U.S. troops in Iraq, training and advising Iraqi forces as part of a global coalition.