Both attacks were claimed by the Islamic Resistance in Iraq, a loose formation of armed groups affiliated with the Hashed al-Shaabi coalition of former paramilitaries that are now integrated into Iraq's regular armed forces.

These pro-Iran groups violently oppose US backing for Israel in its war against Hamas in the Gaza Strip, which erupted on October 7 when the Islamist group launched a deadly attack into Israel.

The United States leads the international coalition battling jihadists in Iraq and neighbouring Syria, and its forces have come under repeated attack in recent weeks.

On Monday in western Iraq, a drone attack targeted the Ain al-Asad airbase, without causing casualties or damage, the US military official said, speaking on condition of anonymity.

And in northeast Syria, "several rockets" were fired at a base in the Al-Shaddadi region, the official added.

Washington has recorded at least 92 attacks in Iraq and Syria since October 17, 10 days after the war between Israel and Hamas broke out.

Early on Friday, salvos of rockets were fired at the American embassy in Baghdad's heavily fortified Green Zone for the first time since the Gaza war began.

At least five attacks targeted US troops and the international coalition in Syria and Iraq that day.

On Saturday the Iran-backed Hezbollah Brigades issued a statement saying the attacks represented "new rules of engagement", and that they would continue until the last American soldier left Iraq.

There are roughly 2,500 US troops in Iraq and some 900 in Syria as part of international efforts to prevent a resurgence of IS.

US Defense Secretary Lloyd Austin has accused the Hezbollah Brigades and another pro-Iran group, Harakat al-Nujaba, of being behind most of the attacks on coalition personnel.

A US statement on Friday following a call with Iraq's Prime Minister Mohammed Shia al-Sudani said Austin stressed "that the United States reserves the right to act in self-defence against those launching any attack against US personnel".

The Pentagon has launched several strikes against fighters belonging to both groups in Iraq, as well as in Syria against sites linked to Iran.

On Friday, Sudani in a statement said targeting embassies "is unacceptable", and called on Iraq's security forces to track down those who fired rockets at the American embassy so they could be brought to justice.