The administration has backing from Republican Senate leader, Mitch McConnell. He's the most influential voice in Congress on Myanmar policy, and in August declared support for "a modest, targeted military-to-military relationship."
But other lawmakers are against it, sharing the concerns of activists who argue it would give international legitimacy to a military that has waged a brutal campaign displacing 100,000 civilians in northern Kachin state during the past two years of political opening.
"It is far too soon to initiate military engagement between the U.S. and Burma," Republican Rep. Steve Chabot, chair of a House panel that oversees policy toward East Asia, told Associated Press.
"The Burmese military not only maintains control over the civilian structures of Burma's government, but has extended its hand as a perpetrator of human rights violations against the ethnic minorities that are sweeping the country."
A number of Western nations are already moving ahead. Britain has invited 30 Myanmar officers to a prestigious defense conference. Australia is also pledging basic military engagement to support security sector reform.
Priscilla Clapp, a former U.S. charge d'affaires in Yangon, says standing on the sidelines doesn't serve U.S. interests. "We need to reach into the organization of the military and help educate people and expose them to new ideas," she said.
Before sanctions were applied, the U.S. financed $4.7 million in military sales delivered to Myanmar between 1980 and 1988, and trained 167 officers at American military schools under the International Military Education and Training, or IMET a program jointly managed by the State Department and Defense Department that helps more than 120 countries.
While the IMET alumni have rarely been movers and shakers in Myanmar's xenophobic military hierarchy, they include a current vice president and several senior government officials. The State Department contends that has helped create a constituency for reform and closer ties with the U.S.
But the Government Accountability Office concluded in an October 2011 report that human rights were generally not a priority in IMET training plans. Because of weak monitoring of the careers of IMET graduates, the report said it was not possible to demonstrate the program's effectiveness "in building professionalism and respect for human rights within foreign military forces."
When the Obama administration informed Congress in spring about plans for gradually resuming military ties with Myanmar, both Republicans and Democrats pushed back and urged the administration to move slowly, congressional aides said.
Various budget bills working their way through Congress reflect that unease. A draft House defense authorization bill for the fiscal year starting in October says the Myanmar military's efforts "to end impunity for human rights abuses" should be assessed before going beyond initial dialogue and engagements.
While the State Department says it's too soon for a full resumption of IMET, it does advocate moving beyond dialogue and starting a formal training program. A so-called Extended IMET program would contribute to military reforms by teaching about human rights, military justice and humanitarian assistance, it says.
Legislative obstacles remain, and endorsement of Suu Kyi, who is revered in Washington, would also be crucial for it to become a reality. She has supported the recent visits by the U.S. Defense Institute of International Legal Studies to Myanmar.
Despite their common loathing for the government's armed forces, Myanmar's myriad ethnic minorities groups have varying opinions about the merits of U.S. military engagement. That's reflected even within the United Nationalities Federal Council an umbrella group that represents various ethnic rebel groups seeking more autonomy within Myanmar.
Khin Maung, the council's deputy head of foreign affairs from western Arakan state, was skeptical the U.S. would be able to change what he calls the entrenched chauvinism of Myanmar's military against minorities. But David Tharckabaw, a council vice president from Karen state, was hopeful U.S. training could turn the military from "bandits" to a disciplined army that is responsible for national defense while respecting human rights.
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Associated Press writer Grant Peck in Bangkok, Thailand, contributed to this report.