The US military handed over control of once brutally violent Anbar province to Iraqi forces Monday - marking a major milestone in America's plan to eventually send its troops home. But American officials warned that the struggle against al-Qaida in Iraq and other insurgents was not over in the western region, the scene of some of the bloodiest battles in Iraq since the 2003 US-led invasion. "This war is not quite over, but it's being won and primarily by the people of Anbar. Al-Qaida has not been entirely defeated in Anbar, but their end is near and they know it," said Marine Maj. Gen. John Kelly, the top US commander in Anbar, during the handover ceremony. The return of security control to Iraqi authorities doesn't mean US troops, who number about 25,000 in the region, will leave Anbar. The vast, mostly desert region extends from the western outskirts of Baghdad to the borders of Syria, Jordan and Saudi Arabia. But US troops will cut back on security patrols and focus on training Iraq's army and police. For years, Anbar, the 11th of 18 provinces to switch to Iraqi control, was the center stage of the Sunni insurgency. The city of Fallujah became the symbol of Sunni resistance until it fell to American troops in November 2004 in the most intense urban combat of the war. The province was the base of the shadowy al-Qaida in Iraq and its leader, Abu Musab al-Zarqawi, who used the area as a staging ground for attacks in Baghdad until he was killed in a 2006 US airstrike. Just two years ago, a Marine intelligence report concluded that al-Qaida had made such inroads that the war was "lost" in Anbar. But later that year, some in the region's Sunni Arab community mounted a backlash against al-Qaida in Iraq. Many Iraqi tribal leaders opposed al-Qaida's brutal tactics, including mass killings of Shiite civilians and of some Sunni leaders who refused to accept al-Qaida's rule. The disaffected Sunni sheiks organized so-called awakening councils that joined forces with US troops to push al-Qaida from the province. That enabled US forces to gain control of the provincial capital of Ramadi and other cities long considered killing zones. Now Anbar is considered one of the quieter parts of Iraq. Yet bitterness remains between the awakening councils and the central Baghdad government, predominantly Shiite. That could complicate larger nationwide political reconciliation efforts. During Monday's ceremony, for example, the head of the local awakening council complained that the central government was not giving Sunni tribesmen enough credit for fighting al-Qaida, and placing too much attention on their past ties to Saddam Hussein. Monday's ceremony had been postponed several times in recent months, with delays blamed on weather and a last-minute disagreement between the governor and the central government over control of security forces. But security concerns also played a role. As recently as late June, a suicide bomber wearing a police uniform killed more than 20 people, including three Marines and several prominent pro-US tribal leaders, in the town of Karmah, 20 miles (32 kilometers) west of Baghdad. Meanwhile in Baghdad, a senior aide to Prime Minister Nouri al-Maliki said Iraq has submitted a list of proposals to tweak a draft of a US-Iraqi security agreement. The changes were submitted to the US government in Baghdad, said the aide, who spoke on condition of anonymity because he wasn't allowed to release the information. US and Iraqi officials have said the two sides agreed tentatively to a schedule that included a broad pullout of US forces by the end of 2011. But al-Maliki has suggested that his government is still not satisfied with that arrangement.