Washington has been concerned by a recent spate of attacks on Iraqi bases where some 5,200 US troops are deployed to help Iraqi forces ensure militants do not regroup.
The attacks, targeting either bases or the US embassy in Baghdad, have averaged more than one per week over the past six weeks.
Two rockets hit the Al-Balad air base, north of Baghdad, late Thursday, Iraqi security forces said.
It came as Washington considers deploying between 5,000 and 7,000 fresh troops to the Middle East to counter its arch-foe Iran, a US official told Agence France Presse.
Thursday's attack with Katyusha rockets did not cause any casualties or material damage but "came close," a US official said.
"There is a spike in rocket attacks," a second US official said, adding that although they had caused no US casualties and little damage, they were increasingly worrying.
Five rockets hit Al-Asad air base on December 3, just four days after Vice President Mike Pence visited troops there.
Security sources said they believed Kataib Hezbollah, a powerful faction close to Tehran and blacklisted by Washington, was responsible.
More than a dozen rockets hit the Qayyarah air base in northern Iraq last month, one of the largest attacks in recent months to hit an area where US troops are based.
There has been no claim of responsibility for the attacks and Washington has not blamed any particular faction, AFP said.
But US Secretary of State Mike Pompeo has blamed similar attacks on Iran-aligned groups.
Iran holds vast sway in Iraq, especially among the more hardline elements of the Popular Mobilization Forces (PMF), a paramilitary force backed by Tehran.
Asked whether the repeated rocket attacks made the PMF a bigger threat to US troops than ISIS, the official agreed. "It is," he said.
Multiple US diplomatic and military sources have told AFP of their growing frustration with such attacks.
They say they are relying on their Iraqi partners to play a "de-conflicting" role between them and the PMF to prevent any clashes.
That is a complicated task, as the PMF has been ordered to integrate with the regular security forces but many of its fighters continue to operate with some independence, AFP said.
"We all recognize the danger out here. Sometimes our Iraqi partners say, well what can I do?" the official said.