The UN has told Myanmar's military junta that "the right of peaceful assembly must fully be respected" as protests rage on across the country. 

In a phone call on Monday night, 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 military junta there has been regularly blocking Internet access to try to stifle dissent since a coup on February 1.

The junta says it overthrew elected leaders, including longtime leader Aung San Suu Kyi, due to alleged voter fraud. It has not yet provided any evidence to support these claims.

Much of the country has been in uproar since soldiers detained San Suu Kyi and her top political allies, ending a decade-old fledgling democracy after generations of junta rule. 

The Nobel laureate, who spent years under house arrest under an earlier dictatorship, has not been seen in public since she was detained on February 1 alongside top aides

The UN'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 in the streets.

Demonstrators have been encouraging civil servants to join the civil disobedience movement in the main city of Yangon.

Earlier, military authorities announced stiff penalties for those opposing the coup leaders.

Myanmar security forces fired on a protest and arrested journalists in the country's north on Sunday as reports of troop movements suggested an impending crackdown on demonstrations against a recent military coup.

Soldiers fired tear gas then shot at a crowd who gathered in Myitkyina to stop a rumoured shutdown of the northern city's electricity grid. A journalist at the scene said it was unclear how many had been injured in the incident. 

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