The document - the veracity of which cannot be independently verified - was obtained by Burmese exiles in Thailand and passed to Guardian Unlimited.
"On behalf of the armed forces, we declare our support for the non-violent action of the Buddhist monks and members of the public and their peaceful expression," it said.
"We are all encountering crisis in the economy and in society, political difficulties of various kinds of oppression. Those realities not only affect the public and Buddhist monks. We in the military are also affected."
Burmese exiles in Thailand, who translated the letter, said it was a source of encouragement to the anti-government movement.
They claimed Burma's military rulers were so concerned by mutiny in the army that they had ordered the arrest of the colonel in charge of governing Rangoon.
Any sign of dissent within the ranks would be a cause for alarm for the three-man military junta. The junta is led by 74-year-old General Than Shwe, who has been acting as the head of state since 1992, and the military has ruled Burma since 1962.
When he became head of state, Gen Than Shwe appeared to be more liberal than his predecessor, General Saw Maung.
He freed some political prisoners and allowed human rights groups to visit Burma. However, he remains resolutely opposed to any role for Aung San Suu Kyi, the opposition leader who has been under arrest for more than a decade.
Gen Than Shwe's career included a stint in the department of psychological warfare. Said to be superstitious, he reportedly consults astrologers. Generals Maung Aye and Soe Win, both hardliners, complete the triumvirate.
The junta reinforced its reputation for paranoia by moving the capital deep into the mountainous jungle at Naypyidaw, outside the town of Pyinmana and 230 miles north of Rangoon.
Activists said the move was designed to insulate the generals from decades of misrule.