Two rockets fell on Wednesday inside Baghdad's heavily fortified Green Zone, which houses government buildings and foreign missions, but caused no casualties, the Iraqi military said.

Sirens were sounding inside the Green Zone. Police sources told Reuters at least one of the rockets fell 100 metres (yards) from the US Embassy.

"Two Katyusha rockets fall inside the Green Zone without causing casualties. Details to follow," the military said.

Two loud blasts followed by sirens had been heard in Baghdad, Reuters witnesses said. Just before midnight, AFP correspondents in Baghdad heard two loud blasts followed by the wailing security sirens of the Green Zone.

There was no immediate claim of responsibility.

The attack came nearly 24 hours after Tehran launched ballistic missiles at Iraqi bases housing American and other coalition forces, which did not cause casualties.

The strikes were in retaliation for a US drone strike that killed top Iranian general Qasem Soleimani and Iraqi commander Abu Mahdi al-Muhandis last week.

Muhandis had been the deputy head of the Hashed al-Shaabi, a web of armed groups incorporated into the Iraqi state but which also have close ties to Tehran.

The United States had accused Hashed groups of being behind a string of rocket attacks on the US embassy in Baghdad and bases hosting American troops across the country.

On Wednesday, the Hashed's hardline factions vowed they, too, would take revenge for the US raid.

Paramilitary chief Qais al-Khazali — blacklisted as a "terrorist" by the US — said Iraq's response to the US "will be no less than the size of the Iranian response". Harakat al-Nujaba, a hardline Hashed faction, vowed to avenge Muhandis.

"To American soldiers: Do not close your eyes. Revenge for the martyr Muhandis is coming at the hands of Iraqis — until the last soldier among you leaves," it said.

Oil prices climb

Oil prices climbed on Thursday after the rocket attack on Baghdad triggered fresh concern over the potential for conflict in the Middle East.

But gains were muted as Washington and Tehran looked to defuse a crisis in the crude-producing region.

Brent crude futures rose 43 cents, or 0.7 per cent, to $65.87 a barrel by 0109 GMT, after seesawing through Wednesday to end with a 4.1pc tumble.

They are now a little down on prices before the Jan 3 killing of Iranian military commander Qassem Soleimani in a US drone attack that sparked the crisis.

West Texas Intermediate futures added 61 cents, or 1pc, to $60.22 after falling nearly 5pc in the previous session.

"We need to be guarded about further sharp declines this week, as we will probably see more activity by proxy militias in Iraq," said Stratfor oil analyst, Greg Priddy.

Still, he said, "our view remains that in the absence of actual losses from conflict with Iran, the market will see mild downward pressure in Q1 on inventory builds".

That pressure was evident on Thursday as a result of a surprise build in US crude stockpiles last week.

Crude oil stocks were up by 1.2 million barrels in the week ended Jan 3 to 431.1 million barrels, against analysts' forecasts in a Reuters poll for a 3.6 million-barrel drop.

Meanwhile JP Morgan maintained its forecast for Brent to average $64.50 a barrel this year.

"The impact on oil prices will depend on (the) extent of supply disruption versus available spare capacity, global oil inventories and reaction to oil price from US producers," the bank said in a commodities research note.