WASHINGTON — The Islamic State has lost 45% of the territory it once held in Iraq and 20% of areas it controlled in Syria, according to new estimates by a U.S.-led coalition combating the extremist group.

Those slow but steady battlefield losses in Iraq are prompting the Islamic State to strike back against civilians with terrorist bombings, the latest killing dozens in Baghdad on Tuesday.

The territory seized by Iraqi forces, aided by coalition airstrikes and advisers, is up from 40% announced earlier this year, according to the latest estimates, which had not been made public before. The percentages are based on areas the militants controlled at their peak strength after they swept into Iraq in 2014.

In Syria, the Islamic State’s losses are up from the coalition’s estimates of 10% to 15% of areas it controlled earlier this year. The group’s de facto capital is in Syria, where the Islamic State, other rebel groups and the Syrian government have waged a five-year-long civil war.

In recent weeks, U.S.-aided Iraqi forces pushed militants out of towns in western Iraq’s Euphrates River valley as they consolidated gains made last December, when Iraq’s army retook the city of Ramadi.

Iraqi forces have begun operations around Mosul, Iraq’s second largest city, in preparation for a major offensive to drive the militants out.

Progress has been slower in Syria, where the U.S.-led coalition cobbled together rebel groups to build a ground force capable of taking on the Islamic State. The size of that force is growing and the Pentagon reported a string of recent successes in northeastern Syria.

The Iraqi military’s gains coincide with a string of terror bombings in and around Baghdad this year. In just the past week, 200 people were killed, including at least 69 Tuesday, according to the Associated Press. The Islamic State claimed responsibility for most of those attacks.

“These bombings are a reaction to the increasing territorial pressure the Islamic State is coming under,” said Matthew Henman, head of IHS Jane’s Terrorism and Insurgency Centre.

The terror bombings in Baghdad are a return to the group’s roots, said Ismael Alsodani, a retired Iraqi brigadier general who served as a military attache in Washington. The Islamic State grew out of al-Qaeda in Iraq, an insurgent group of Sunnis that battled U.S. forces after the overthrow of dictator Saddam Hussein in 2003.

Some of the recent bombings targeted Shiite neighborhoods, an echo of al-Qaeda’s strategy to stir sectarian tensions, Alsodani said. In 2006, terror strikes against Shiites helped trigger a larger conflict between Shiites and Sunnis throughout Iraq.

The Islamic State distinguished itself from al-Qaeda by fielding troops, capturing cities and creating a government as part of a plan to establish a caliphate throughout the region. When it swept into Iraq from Syria in 2014, it resembled a conventional military force that operated in large formations and employed heavy weapons.

But nearly two years of relentless airstrikes and pressure from Iraqi ground forces have forced the militants to move in smaller groups and retreat from some of the territory they controlled. “Their ability to conduct large-scale offensive operations has primarily stopped,” said Army Maj. Gen. Gary Volesky, a top commander in Iraq.

It is not clear yet whether the militants will survive by continuing to launch terror attacks in Baghdad and elsewhere, Henman said. “It may be that this is the group adapting and accepting that it is no longer able to expand and seize more territory,” he said.