BAGHDAD — Iraq’s prime minister hailed ‘‘big successes’’ Monday by government troops after launching an offensive to retake Fallujah from Islamic State militants, but the operation promises to be one of the toughest challenges yet for the country’s struggling security forces.
Troops recaptured some agricultural areas in Garma, a district along the northeastern edge of Fallujah, under intensified Iraqi airstrikes and heavy artillery, said Colonel Mahmoud al-Mardhi, who leads Shi’ite militia forces in the operation.
The US-led coalition carried out two airstrikes, the Pentagon said, part of an aerial campaign that has seen an average of two bombings a day over the past week in the city about 40 miles west of Baghdad.
Prime Minister Haider al-Abadi toured the Fallujah front line dressed in the all-black fatigues of Iraq’s elite counterterrorism forces, saying the troops had achieved ‘‘more than what was planned for,’’ and ‘‘big successes,’’ but he did not elaborate.
He had triumphantly announced the start of the operation in a televised address late Sunday night, flanked by senior military commanders. Since January 2014, the city has been under the control of Islamic State militants, also known as ISIS.
‘‘The Iraqi flag will be raised high over the land of Fallujah,’’ he vowed, saying it would be taken back from those who ‘‘kidnapped’’ it.
Originally planned to start more than two months ago, the offensive was delayed by political infighting and the deteriorating security situation in Baghdad, Abadi said.
Navy Captain Jeff Davis, a Pentagon spokesman, said he does not believe the Iraqis have gotten into the city yet.
The latest estimates put the number of ISIS fighters in all of Anbar province at about 1,000 and ‘‘dropping quickly,’’ Davis said. The number of fighters in Fallujah also has been falling, he said, but he added that he did not have a firm number. One previous coalition estimate put it at 500 to 700 fighters.
Fallujah will be the most difficult fight yet for the Iraqi military, which is still struggling to regroup after a collapse in the face of the ISIS assault on Mosul nearly two years ago.
After more than two years in firm control of Fallujah, Islamic State fighters are expected to have knitted their way into the civilian population on a greater scale than previously seen in Ramadi or Tikrit.
The Fallujah offensive follows a series of territorial gains over ISIS in western Iraq, but it still could delay plans to win back the second-largest city of Mosul, the focus of the US plan to defeat the militants in Iraq and neighboring Syria.
A number of other operations announced by Iraqi leaders have faltered. A plan to retake Mosul was announced in March with much fanfare, but only a handful of villages near the city have been captured since then.
The assault on Fallujah is the first major offensive in an urban area since Iraqi forces cleared Ramadi of ISIS fighters earlier this year. Despite being declared a victory, Ramadi stands largely uninhabitable.
ISIS explosives and a punishing campaign of airstrikes destroyed thousands of homes and buildings, and many still standing are suspected of being booby-trapped. More than 100 civilians died trying to return to Ramadi after ISIS was pushed out.
Ramadi was under ISIS control for less than a year, but the extremists have controlled Fallujah for more than twice that time. The predominantly Sunni provincial capital was the first Iraqi city to fall to ISIS, and it has long been opposed to the Shi’ite-led central government in Baghdad.
During an insurgency waged by the ISIS group’s predecessor, Al Qaeda in Iraq, Fallujah was the scene of some of the bloodiest urban combat with US forces. In 2004, more than 100 US troops died and another 1,000 were wounded fighting insurgents in house-to-house battles.
Once home to more than 250,000 people, only about 60,000 to 100,000 civilians remain in Fallujah, according to the coalition and the United Nations. Many Iraqis are suspicious of the civilians who have not fled, assuming many are ISIS sympathizers.
