MOSUL, Iraq — The shooting had ended, the smoke had cleared, and as they trooped one by one to the microphone to critique the live fire exercise, the Iraqi generals issued a warm greeting to their comrades in arms.

"My brothers, my friends," each began.

"That's us," said Col. Brian Winski, the U.S. commander at Contingency Operating Site Marez, just outside Mosul. "It's absolutely sincere."

It's eight years since the United States conquered Iraq, overthrew Saddam Hussein and unintentionally touched off a sectarian war that killed more than 4,470 U.S. troops, 8,200 Iraqi security forces and upward of 50,000 Iraqi civilians, according to icasualties.org, a website that tracks deaths in the war.

As enormous a blunder as the March 2003 invasion may have been, however, the withdrawal of U.S. troops, accelerated by President Barack Obama, has fostered something U.S. diplomats weren't expecting: a relationship of mutual respect. And many Iraqis, though certainly not all, think this could provide the basis for a long-term alliance.

A fledgling democracy in a volatile neighborhood, Iraq's democratically elected government is contemplating asking the U.S. to leave behind some of the 46,000 troops now packing to leave. Training of Iraqi forces, which went into high gear early this year, is one of the major reasons.

With their detailed scripts and careful staging, training exercises may lack drama, but they're a prime source of the skills needed in military operations. The U.S. military excels in this area and views its relations with the Iraqi military as the "lynchpin of a strategic partnership" for decades to come," Winski said.

Many Iraqi military officials say they need at least some U.S. forces to stay behind.

"We still need help from coalition forces, for example with air cover. We want to be on the same level as countries on our borders, and we need help, joint training or new ideas," said Gen. Riad Jalal Tawfiq, deputy commander of the Iraqi Ground Forces Command in Baghdad.

They also need intelligence support and help developing logistics, maintenance and support capabilities, said Maj. Gen. Jeffrey Buchanan, chief U.S. military spokesman.

At the same time, some politicians would prefer to see the backs of the U.S. forces. Athiel al Nujaifi, the governor of Ninewah province, which includes Mosul, believes that U.S. troops are no longer needed in the city or the province.

Iraq's second biggest city, with a population of 1.8 million, Mosul is mostly Sunni Muslim and has a major insurgency — as many as 800 active al Qaida-linked fighters, according to U.S. officials, or possibly only 100, according to Nujaifi.

"I am confident that we are able to keep the peace without any assistance from the American forces," Nujaifi said in a phone interview. "It is we who demanded that they withdraw from Mosul, and not more than a month later, security became noticeably better. And we are confident that the same will happen all over the province as soon as they withdraw from all of Ninewah."

Winski said: "I think it is safe to say that the provincial governor is the most vocal, and most likely the first, to express desire for U.S. forces to leave." But he noted that the U.S. is helping the Iraqi security forces secure Mosul, the surrounding areas and the rest of the province, providing intelligence, support and training in specialty skills.