Matthew Daley, deputy assistant secretary of state for East Asian and Pacific Affairs, told a congressional panel the United States had raised its "concerns" with Myanmar, formerly known as Burma, over such moves.
"We have reason to believe that the DPRK (North Korea) has offered surface-to-surface missiles" to Myanmar, Daley said.
"We have raised this issue of possible missile transfers with senior Burmese officials and registered our concerns in unambiguous language," he told US lawmakers.
"Although Burmese officials have indicated that they have not accepted offers of such weapons systems, we will continue to monitor the situation and will deal with it vigorously and rapidly."
Stalinist North Korea and the junta in Yangon already have what Daley called "a military and trade" relationship.
Daley said Washington was also aware "that the Burmese regime is interested in acquiring a nuclear research reactor." But he said news reports of "construction activities are not well founded."
Myanmar said in January 2002 that it was planning to build a nuclear research reactor to be used "for peaceful purposes" and that it was negotiating with Russia.
A senior aide to the chairman of the US Senate Foreign Relations committee last month raised the alarm over possible nuclear links between North Korea and Myanmar.
Keith Luse, a senior aide to Senator Richard Lugar, warned that US policymakers must pay "special attention" to what he said was a growing relationship between the Stalinist state and the military government in Yangon.
Luse questioned whether Pyongyang was selling Scud missiles to or through Myanmar.
Myanmar last year rejected a report that it was receiving missiles and nuclear technology from North Korea, saying it did not need such arms as it was "everybody's friend."
Daley said the US government noted news reports of Myanmar providing heroin as compensation for transfers of military or nuclear technoloy or equipment but "available evidence simply does not support such a conclusion."
The United States had imposed sanctions on Myanmar last year, including an import ban, asset seizure and ban on financial services.
Daley said following the economic sanctions, the US Treasury Department had blocked 13.3 million dollars worth of transactions.
The financial services ban had forced Myanmar banks to shift from US dollar to Euro-denominated letters of credit and remittances while many traders turned to unofficial channels to conduct dollar transactions, he said.
"Our sanctions represent a clear and powerful expression of American dismay at the developments in Burma last year," he said. "No other country has taken like measures."
The sanctions came after Myanmar's opposition leader and democracy icon Aung San Suu Kyi was detained on May 30, 2003 following a violent ambush on her National League for Democracy (NLD) supporters by a junta-backed mob.
Her detention precipitated a crackdown on the party which led to an international outcry. The party of 58-year-old Aung San Suu Kyi, who remains under house arrest, won a landslide 1990 election victory but was never allowed to rule.