The recent successes in quieting violence in Basra and Sadr City appear to be stretching to the long-rebellious Sunni Arab district here in Mosul, raising hopes that the Iraqi Army may soon have tenuous control over all three of Iraq’s major cities.

In this city, never subdued by the increase of American troops in Iraq last year, weekly figures on attacks are down by half since May 10, when the Iraqi military began intensified operations here with the backing of the American military. Iraqi soldiers searching house to house, within American tank cordons, have arrested more than 1,000 people suspected of insurgent activity. The Iraqi soldiers “are heady from the Basra experience,” Brig. Gen. Raymond A. Thomas III, the commander of American forces in Mosul, said in an interview. “They have learned the right lessons.” The crucial lesson, in fact, over the past month appears to be that all sides — the Iraqi military as well as various insurgent groups — prefer, at the moment, not to fight. Rather, as in Basra and Sadr City, the huge Shiite enclave in Baghdad, the Iraqi military appears to have allowed many insurgents to slip out of Mosul, after scores of negotiations with militias and their leaders. This approach could make any gains temporary: The insurgents, here as elsewhere, are alive to fight another day. And little progress has been made on political reconciliation among rival sects and ethnic groups that could help reduce violence in the long term..........