"Acts of violence like those perpetrated and attempted over the past week have no place in civilized society," the U.S. Embassy said in a statement.
"We are confident in the people of this country to confront such acts of terror with strength, determination and a continued commitment to national peace, development, and reconciliation."
There have been four arrests, but it remains unclear who is responsible for the explosions. The Myanmar government is still fighting Kachin and other scattered ethnic groups and the country has been struggling with sectarian violence between Buddhists and Muslims.
The first bomb in Namkham went off at around midnight Wednesday in the center of town, but no one was hurt. The second and third followed in quick succession in the same area at around 7:30 a.m. Thursday.
The officer at the local police station said one man was killed in those blasts and six others wounded, none of them critically.
They appeared to be low-intensity devices, causing little damage to nearby structures, he said. "They may have been time bombs, but we don't know for sure."
Small bombings occurred frequently in Myanmar during 50 years of military rule. But they have been rare since the nominally civilian government of President Thein Sein took office in 2011 and started implementing political and economic reforms.
Many activists and rights groups, however, say Myanmar is still far from free and the government is struggling to contain sectarian violence and long-running ethnic insurgencies.
The government says the perpetrators are trying to tarnish the image of the country.
So far at least four suspects have been detained.
Thein Sein's spokesman Ye Htut told Radio Free Asia's Myanmar Service they were providing information to police that could lead to more arrests.
He said it was not yet clear if the suspects held so far were connected to one another.
