Radical Sunni militants aligned with Al Qaeda threatened on 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 put out calls over mosque loudspeakers for men to join their struggle in both cities in western Anbar Province, which were hugely important battlegrounds during the American-led war in Iraq and remain hotbeds of Sunni extremism. The fighting in Ramadi and Falluja had implications that extended beyond Anbar’s borders, as the Sunni militants fought beneath the same banner as the most hard-line jihadists in Syria — the Islamic State of Iraq and Syria, or ISIS. That fight, and a deadly bombing in Beirut on Thursday, was the latest evidence that the Syrian civil war was breeding bloodshed and sectarian violence around the region, destabilizing Lebanon and Iraq while fueling a resurgence of radical Islamist fighters. The number of casualties in Anbar was unclear amid the unfolding chaos, but officials in hospitals in the province reported that at least 35 people were killed on Thursday and more than 70 others were wounded. The fighting began several days ago after Prime Minister Nuri Kamal al-Maliki, a Shiite, ordered security forces to dismantle protest encampments in Falluja and Ramadi.