AFP reporters in the Iraqi capital's east heard at least five booms, followed by whistling sounds.

A few moments later, they heard thunderous rapid-fire sounds and saw streams of red flares in the night sky, indicating the US embassy's C-RAM rocket defence system had been activated.

A security source told AFP at leat three rockets hit near the US diplomatic mission, while two others hit separate residential neighbourhoods.

Iraq's security forces issued a statement saying the attacks caused material damage, but no casualties.

The attack is the third on US military and diplomatic installations since a truce in October largely put an end to a year of rocket and roadside bomb attacks on foreign installations across Iraq.

The first, on November 17, saw a volley of rockets slam into the US embassy and various parts of the Iraqi capital, killing one young woman.

On December 10, two convoys transporting logistical equipment for the US-led coalition helping Iraqi troops fight jihadists were targeted with roadside bombs.

The attacks have been claimed by groups that both US and Iraqi officials have described as smokescreens for well-known Iran-aligned armed factions in Iraq.

Tensions have been high ahead of January 3 anniversary of the 2019 US drone strike in Baghdad that killed Soleimani and leading Iraqi paramilitary figure Abu Mahdi al-Muhandis.

The US diplomatic mission has already partially withdrawn its staff due to security concerns, two senior Iraqi officials told AFP earlier this month.

They described the move as a "minor drawdown based on security reservations from the US side," and said it was not a rupture of diplomatic ties.

Iraqi and Western officials see a turbulent few weeks ahead of the White House handover from President Donald Trump, who has pursued a "maximum pressure" policy against Iran that has also squeezed its allies next door in Iraq.

They did not rule out last-minute military action by the Trump administration on Iranian interests in Iraq, or a possible escalation by Iran-backed groups around Baghdad.