IRBIL, Iraq — Iraq opened the next chapter in its offensive to drive the Islamic State out of Mosul on Sunday, launching a major air and ground assault on the western half of the city.

Overnight, planes carpeted the ground with leaflets, directly appealing for the surrender of fighters in the militant group, also known as ISIS.

“To those of you who were intrigued by the ISIS ideology,’’ one of the leaflets said, “this is your last opportunity to quit your work with ISIS and to leave those foreigners who are in your homeland. Stay at home, raising the white flags as the forces approach.’’

On state-run television, Prime Minister Haider al-Abadi of Iraq announced the beginning of the offensive, describing it as “a new dawn’’ and calling on his troops “to move bravely forward to liberate what is left of the city.’’

Mosul, once Iraq’s second-largest city, is the last major ISIS stronghold in Iraq. Its occupied western sector is still heavily populated, with about 600,000 civilians remaining, according to UN estimates.

Iraqi ground units entered the village of Athba, about 3 miles southwest of Mosul’s international airport, on Sunday, encountering only light resistance. Separately, the Iraqi Army’s 9th Division moved into the village of Bakhira, also southwest of the city, the Ministry of Defense said.

The US-led coalition has been providing air support throughout the four-month-old Mosul offensive and carried out nine airstrikes near Mosul on Saturday.

The assault is taking place amid new concerns about the condition of hundreds of thousands of civilians still trapped in the western part of the city. Food, water, and cooking fuel have all been reported to be in short supply, and residents have described increased harassment from Islamic State fighters preparing for the attack.

The overall push to free Mosul began in October, with local troops pushing from the east into the city’s geographically larger but more sparsely populated eastern half.

In late January, they reached the banks of the Tigris River, which bisects Mosul, and declared the city’s eastern section liberated.

The operation took longer than expected and took a high toll on civilians and the Iraqi forces, but much of the city’s infrastructure was preserved and a sense of daily life has returned.

That is in contrast to the operations to take back other cities from the Islamic State, including Ramadi and Sinjar, which were laid waste by airstrikes. More than a year since Sinjar was freed, even its mayor has not been able to return.

The fight for Mosul’s western half could be even more protracted than for its east. The west is home to neighborhoods of narrow streets, some so small that it will not be possible for Iraqi troops to enter in their fortified Humvees.

That may make the Islamic State’s signature suicide bomb attacks even more effective.

Because all five of the bridges spanning the Tigris have been bombed, Iraqi troops will trace a circuitous path to western Mosul, initially approaching it from the city’s south.

Officials said the first objective would be the airport, just south of the city. By midday Sunday, Iraqi forces had captured a string of nearby villages, advancing within 6 miles of the airfield, officers from the troops said.

“The US forces continue in the same role as they did in East Mosul,’’ Defense Secretary Jim Mattis told reporters traveling with him Sunday, adding that the rules of engagement for US troops in Iraq had not changed: “We are very close to, if not already engaged in, that fight.’’

He said that the US-backed coalition fighting the Islamic State would “continue with the accelerated effort to destroy’’ the group.

Anticipating the offensive, the Islamic State damaged the Mosul airport, carving wide trenches onto the runways and adjacent taxiways and aprons, leaving no paved portion usable by aircraft, according to an analysis of satellite imagery by Stratfor, a global intelligence company.

While the airport may be unusable, taking it would be a milestone for the offensive, as would taking the adjacent hilltop village of Abu Saif, which sits at a higher elevation than Mosul. Because of the Islamic State’s heavy use of snipers, securing high ground is crucial, and Iraqi forces were nearing the base of the hill by Sunday afternoon.

The troops’ push into western Mosul will be further complicated by the Islamic State’s vast network of tunnels throughout the city, allowing fighters to hide from overhead surveillance. And the group is also increasingly using armed drones, allowing them to spot and remotely bomb advancing Iraqi troops.

The Islamic State has become better at the use of small drones, which are available off-the-shelf in malls across the region.

They use the drones to pinpoint army positions and to target them, and recently recovered Islamic State documents show how the group has cobbled together its own drone program.

“Mosul would be a tough fight for any army in the world, and the Iraqi forces have risen to the challenge,’’ Lieutenant General Stephen Townsend, the commander of the US-led effort against the Islamic State, said in a news release from US Central Command announcing the beginning of the operation. Some of the 450 US advisers on the ground in Iraq are helping Iraqi officers plan and execute the offensive.