A U.S.-led air coalition has been bombing Islamic State positions across Iraq, supporting Baghdad's ground forces and its poorly equipped air force.
On Sunday, it sharply stepped up air strikes around Ramadi, with 29 out of 39 missions in Iraq targeting Islamic State positions near the city.
Iraq has sought to redress its own lack of air power by purchasing F-16 fighter jets from the United States, but deliveries of the 36 aircraft were delayed because of security concerns after the Islamic State offensive last summer.
On Monday, a first batch of four F-16s landed at Balad air base north of Baghdad, an Iraqi air force officer said. Authorities said the planes would join operations in Anbar within days.
Hadi al-Ameri, commander of the largest Shi'ite force, the Badr Organization, told Iraqi television on Sunday he expected the main assault on Falluja to take place after the Eid holiday, which starts later this week.
Residents in Falluja and Ramadi reported heavy bombardment of both cities early on Monday.
“Arrival of four F-16s at Balad air base,” read a flash on the ministry’s website, in an announcement also confirmed to AFP by the prime minister’s office.
Brett McGurk, US President Barack Obama’s deputy envoy for the international coalition against the Islamic State (IS) jihadist group, also confirmed the jets had arrived.
“After years of preparation & training in the U.S., Iraqi pilots today landed the 1st squadron of Iraqi F16s in #Iraq,” he said on social media.
The delivery had most recently been delayed over security concerns at Balad, which lies about 70 kilometres (45 miles) north of Baghdad.