A major offensive to recapture the key Iraqi city of Fallujah from the Islamic State is underway, with U.S. airstrikes pounding the area while Iraq sends in 20,000 troops and federal police forces, in addition to Shiite militia.

The Wall Street Journal reports on progress after the first day of the campaign:

By late Monday, the Popular Mobilization Forces had taken over two districts on Fallujah’s outskirts, said Col. Mahmood al-Jumaili, a commander for the group, which includes militias.

An Islamic State communications center was destroyed and 34 of the group’s fighters were killed, including a senior leader, the Iraqi military’s Joint Operations Command added. The death toll couldn’t be independently verified, and the government gave no indication of casualties on its side.

The U.S.-led coalition said it conducted two strikes near Fallujah, targeting Islamic State’s weapons facilities and destroying bunkers and tunnel entrances. Pentagon spokesman Capt. Jeff Davis said the coalition has struck 21 targets in Fallujah since May 17.

The Iraqi military said its jets were able to destroy ISIS bomb factories and artillery positions in Fallujah, leading embattled Prime Minister Haider al-Abadi to declare, “The success of the plan has been greater than expected.”

Abadi has been under enormous political pressure due to the deteriorating security situation in Baghdad, culminating in demonstrations during the weekend that put thousands of people on the streets, demanding improved security. Although this weekend’s protests ended with a volley of tear gas and rubber bullets from security forces, the situation was still considered an improvement from the Shiite riots at the end of April.

The Journal cites estimates that ISIS only has about a thousand fighters in Anbar province, as well as about a thousand sympathizers, so if the Iraqis are accurately reporting the size of the force sent to liberate Fallujah, they have a numerical advantage of more than ten to one, backed by U.S. airpower. ISIS forces have also been weakened by a blockade stretching back several months.

Nevertheless, the battle for Fallujah is “expected to be arduous and protracted,” in part because the largely Sunni residents are suspicious of the Shiite militias fighting alongside government forces. There are still about 50,000 civilians in the city, giving the Islamic State plenty of human shields. Even as Abadi was claiming a highly successful first day for the Fallujah campaign, and Iraqi military commanders said they had encountered only “weak” resistance so far, ISIS was claiming to have repelled Iraqi attacks and destroyed some of their military hardware with suicide bombings.

A U.N. spokesman said on Monday that the situation around Fallujah is “very fluid” and that the United Nations is concerned about the risk to civilians caught in the fighting, especially since the Islamic State is doing what it can to prevent them from fleeing.

Iraqi officials said that planting a large number of Improvised Explosive Devices (IEDs) around the city is among the precautions ISIS has taken, both to impede attacking forces and to make it difficult for civilians to flee.