Since Wednesday, at least five rocket and drone attacks have targeted three Iraqi military bases where American troops are stationed as part of the international coalition set up to fight the Islamic State group.

"The attacks that target Iraqi bases that house advisers from the international coalition in Iraq are unacceptable," Iraq's military spokesman Yahya Rasool said in a statement.

Prime Minister Mohamed Shia al-Sudani had "directed all the security services to... pursue the elements responsible for these attacks", he added.

Most of the attacks have been claimed by a group called "Islamic Resistance in Iraq" on Telegram channels affiliated with Shiite factions loyal to Iran, the sworn enemy of Israel.

Militants from the Iran-backed Palestinian Islamist group Hamas poured into Israel from the Gaza Strip on October 7, killing more than 1,400 people, mostly civilians, and taking more than 200 hostages, according to Israeli officials.

Gaza's Hamas-run health ministry said on Monday that more than 5,000 people, also mainly civilians, have been killed in Israel's retaliatory bombardment of the Palestinian territory. Its death toll includes more than 2,000 children.

Without directly mentioning the attacks on the Iraqi bases, the United States, a close Israeli ally, on Friday ordered the evacuation of all non-essential staff from its embassy in Baghdad and consulate in Arbil, in Iraqi Kurdistan.

The Iraqi government is supported by pro-Iran parties, and has repeatedly condemned Israel's strikes on Gaza in retaliation for the October 7 attacks.

But Baghdad needs to preserve its relations with the United States, which has 2,500 troops deployed on Iraqi soil to advise and train the Iraqi army.