The Islamic State terror group's claim that its fighters shot down a U.S. warplane and killed the crew in western Iraq is false, a spokesman for U.S. Central Command told Fox News on Monday.

ISIS made the claim through its news agency, Amaq. The terror group said it shot down the aircraft near Ayn al-Asad Airbase, a U.S.-Iraqi base about 100 miles northwest of Baghdad.

The Pentagon has confirmed that all coalition aircraft are accounted for, a senior defense official told Fox News.

ISIS still controls significant areas in northern and western Iraq, including the country's second-largest city of Mosul. Since its 2014 blitz, the group has declared an Islamic caliphate on the territory it holds in Iraq and Syria.

The Sunni militant group recently stepped up its attacks far from the front lines in what Iraqi officials see as an attempt to distract from their battlefield losses.

Since late last year, the group has suffered a string of losses, most recently in Fallujah, where it was driven out last month by Iraqi forces after occupying the city for more than two years. But the extremists have continued to carry out near-daily bombings in and around Baghdad, as well as complex attacks in other countries.

Fox News' Jennifer Griffin, Lucas Tomlinson and The Associated Press contributed to this report.