The despatch of ambassadors William Brown and Stanley Roth follows Rangoon's adoption of laws which prohibit any attempt to draw up a rival constitution.This would muzzle Ms Suu Kyi's National League for Democracy Party (NLD), which has held large rallies outside her house in recent weeks.
The dissident leader, said a State Department spokesman, "has a right, under international law and any reasonable standard of decency, to speak out about conditions in her own country." Washington is also demanding the release of more than 100 NLD activists still in detention.
Britain also expressed concern that about 30 opponents of the military regime remained in detention. "We are also concerned by reports that some have been charged and may be put on trial behind closed doors, including one of Aung San Suu Kyi's close personal aides, U Win Htein," a Foreign Office spokesman said.
The Clinton administration, which has become increasingly outspoken about human rights abuses in Burma, hopes that its move will prod the military junta into dialogue with the opposition. But Washington is also contending with pressure from Congress for more radical action, which could merely provoke a split with its allies.
On Capitol Hill, a bipartisan Bill has been tabled that would bar US investment in Burma entirely.The State Department is opposed to mandatory sanctions, arguing that the US needs to retain the ability to respond to events in Burma.
Washington is infuriated by the failure of the Burmese junta to crack down on narcotics trafficking but must keep an eye on major US investments in the country. The Unocal energy company has a major stake in a $1bn (pounds 700m) offshore gas project. If Congressional sanctions force Unocal to pull out, other foreign companies would simply move in, Unocal's president, John Imle, said recently.
The two US envoys yesterday began their tour of east Asia in Tokyo, where they met the Japanese Foreign Minister, Yukihiko Ikeda.
Japan's support will be vital to Washington as Japanese grant aid and technical co-operation to Burma amounted to $134m in 1994, more than twice the 1993 total.
Many of the biggest names in Japanese business and finance, including C. Itoh, Sumitomo, Mitsui, Fuji Bank and Mitsubishi, have offices in Rangoon.
But yesterday's meeting seemed to produce little. And if past form is anything to go by, Burma is unlikely to receive much more than a brisk ticking-off from Tokyo.
Mr Brown and Mr Roth were scheduled to fly on to the Philippines yesterday, and later to visit Indonesia, Singapore, Malaysia and Thailand.
But in Burma, new billboards appeared denouncing Aung San Suu Kyi. They said she was a foreigners' stooge who should be crushed.