U Aung Min said the government will honor its pledge to end the clashes, particularly in Kachin state, Voice of America reported Thursday.
Aung Min was in Washington to attend a Congressional Gold Medal award ceremony for democracy leader and activist Aung San Suu Kyi, who spent years under house arrest in Myanmar, formerly known as Burma, until her release in 2010.
"The president already promised there will not be offensives apart from some defensive actions. I also tell you the army is strictly following the orders," Aung Min said. "There will be no open-season offensive. I guarantee it."
Aung Min said the military has begun to minimize the potential for conflict by moving troops farther apart.
"Now the positions of the troops [overlap], which lead to misunderstandings and some gunfire," he said. "My objective is to make the troops withdraw from their positions so they are at least 5 kilometers [about 3 miles] apart as required in the primary cease-fire agreement. Only then can people sit to negotiate more."
Questions have been raised about Myanmar's treatment of refugees, many of whom fled to Thailand to escape the fighting, Voice of America said.
Aung Min said the government is working to speed up their return.
"If the areas are secure enough, they will be coming back," he said. "When they come back, they will get back their own, original lands where they used to live."
Myanmar President Thein Sein will be in New York next week to address the U.N. General Assembly.
The United States has considered easing of some sanctions imposed on Myanmar because of the former government's poor human rights record, U.S. officials have said.