In a phone call, UN Special Envoy Christine Schraner Burgener warned that "any form of heavy handed response is likely to have severe consequences".
Access to the internet in Myanmar was restored on Tuesday morning after it had been cut off for a second night.
The junta has been regularly blocking the web to try to stifle dissent since the 1 February coup.
Ms Schraner Burgener's warning came during Monday's phone call with the junta's deputy head Soe Win, a UN spokesperson said.
The special envoy stressed that internet blackouts "undermine core democratic principles".
Protesters were out again early on Tuesday, with news agency Reuters reporting small groups gathering.
They have been encouraging civil servants to join the civil disobedience movement in the main city of Yangon.
Earlier, the military authorities announced stiff penalties for those opposing the coup leaders.
The junta says it overthrew elected leaders, including longtime democracy campaigner, Aung San Suu Kyi, due to alleged voter fraud. It has not provided any evidence to support these claims.