A rocket landed near Baghdad airport overnight but did not explode, an Iraqi security source said, after two other rocket attacks targeted American diplomatic and military installations at the weekend.

However, the Iraqi army said early Monday that no rocket had been fired.

American soldiers are based at the airport. Since October, US diplomats and troops across Iraq have been targeted in around three dozen missile attacks blamed by Washington on pro-Iranian armed factions.

Late last month, in the first move of its kind, elite Iraqi troops arrested more than a dozen Tehran-backed fighters allegedly planning a new attack on Baghdad's Green Zone, home to the American and other foreign embassies.

Iraqi government officials said the raid would help deter future attacks -- but on Saturday night militants made another attempt.

One rocket fired at the Green Zone landed near a home, wounding a child, according to the Iraqi military, which said it had thwarted another attack targeting its Taji base north of the capital.

Those attempts came just hours after the US embassy tested a new rocket defence system, according to a senior Iraqi security source. There was no immediate comment from the embassy on whether the system was used against the rocket.

Iraq has long been caught in a tug-of-war between its two main allies Iran and the US -- arch-enemies whose relations have further crumbled since Washington pulled out of a landmark nuclear deal with Tehran in 2018.

Baghdad carefully balances its ties to the two countries, but the repeated rocket fire risks rocking its tightrope.

The US blames the attacks on Kataeb Hezbollah, a Tehran-backed faction within Iraq's state-sponsored network of armed units known as the Hashed al-Shaabi.