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"Two rounds landed inside the Taiji base and exploded, and a third landed outside it and did not detonate," the source told AFP.

The attack, which was not claimed, comes as Iraq faces a wave of anti-government protests in Baghdad and the south and one day after Washington announced it had killed the Islamic State group's leader, Abu Bakr al-Baghdadi.

The US currently has 5,200 troops in Iraq, part of a US-led international coalition against IS.

Their presence at several bases in Iraq has been the subject of debate, with pro-Iranian Shia militias and politicians making frequent demands for their withdrawal.

Earlier this month, US Defence Secretary Mark Esper said American troops withdrawing from Syria will stay in Iraq "temporarily" before returning to the US.

It is unknown who is responsible for the attack however several mystery strikes have targeted Iraq's Popular Mobilisation Forces (PMF) - a coalition of some 70, mostly Shia militias backed by Iran - in recent months.

Since mid-July, more than five PMF arms' depots and training camps have been targeted in apparent attacks. 

The latest such incident took place earlier this month when unidentified aircraft launched airstrikes on PMF bases near Syria's border.

The PMF have repeatedly blamed Israel for raids by unmanned aircraft, but on Monday, for the first time, Iraq's prime minister also accused Israel of being behind the attacks.

"Investigations into the targeting of some Popular Mobilisation Forces positions indicate that Israel carried it out," Prime Minister Adel Abdul Mahdi was quoted by Al Jazeera as saying.

A spokeswoman for the Israeli military declined to comment on the Iraqi premier's remarks.

US and Middle East intelligence officials confirmed in August that a string of unclaimed attacks against the Shia militia bases in Iraq were carried out by Israel.

Israel has repeatedly bombed Iranian targets in neighbouring Syria, but an expansion of the campaign to Iraq would risk damaging Washington's relations with Baghdad.

Read more: Indepth: Normalisation breeds impunity: Deafening silence as Israel strikes multiple Arab states

Israel has accused Tehran of attempting to establish a land corridor from Iran to Lebanon, via Iraq and Syria, and the strikes appear to correspondent with this alleged supply route.

Iran has a strong military and militia presence in Iraq and Syria and backs Lebanese movement Hezbollah.

The PMF was established in 2014 from mostly-Shia armed groups and volunteers to fight the Islamic State group and is now formally part of Iraq's armed forces.

But the US and Israel fear some units are an extension of their arch-foe Iran and have been equipped with precision-guided missiles that could reach Israel. 

Deadly protests

The latest attack came as Iraq struggled to contain protests across the capital and the predominantly-Shia south of the country.

At least 18 protesters were shot dead on Monday evening and Tuesday morning in the Iraqi city of Karbala, hours after the army announced a nationwide curfew to quell popular anti-government demonstrations that have spread through the country.

The protests have been largely spontaneous and led by young Iraqis angry at poor public services, government corruption, and unemployment in the oil-rich country.

Read more: Indepth: Desperate Iraqi youth renew protests in unyielding attempt to reclaim their homeland

Students at schools and universities across Iraq went on strike on Monday, with one woman killed after being reportedly hit in the head by a tear gas canister fired by security forces.

Prime Minister Adel Abdel-Mahdi has promised a reforms but activists said the steps do not go far enough to tackle endemic corruption that plagues much of the country.

Among the reforms announced by parliament are the cancellation of financial bonuses for top officials, the dissolution of governorate councils pending elections, and the creation of a parliamentary committee to make amendments to the Iraqi constitution.

On Monday, Iraq's parliament speaker Salim Jabouri called on security forces to "protect the lives of protesters and public and private property".

The death toll for the protesters now approaching a hundred following weeks of protests, this appeal appears to have gone unheeded.

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