BAGHDAD — Radical Sunni militants aligned with Al Qaeda threatened Thursday to seize control of Falluja and Ramadi, two of the most important cities in Iraq, setting fire to police stations, freeing prisoners from jail and occupying mosques, as the government rushed troop reinforcements to the areas.

Dressed in black and waving the flag of Al Qaeda, the militants commandeered mosque loudspeakers to call for supporters to join their struggle in both cities in the western province of Anbar, which have increasingly become centers of Sunni extremism since American forces withdrew from the country at the end of 2011.

For the United States, which asserted at the time that Iraq was on track to become a stable democracy, Anbar holds grave historical significance — as a place for America’s greatest losses, and perhaps its most significant success, of the eight-year war.

Nearly one-third of the American soldiers killed in the war died trying to pacify Anbar, and Americans fought two battles for control of Falluja, in some of the bloodiest combat that American troops had faced since Vietnam.