After watching hundreds of thousands of people rally in opposition to last week's coup, junta chief General Min Aung Hlaing made a televised speech on Monday evening to justify seizing power.

The military has banned gatherings of more than five people in Yangon, the nation's commercial hub, the capital of Naypyidaw and other areas across the country where major rallies have erupted, including the second biggest city Mandalay.

A nighttime curfew was also imposed at the protest hotspot sites.

But on Tuesday, fresh protests emerged in various parts of Yangon, including near the headquarters of the National League for Democracy (NLD), the party of deposed leader Aung San Suu Kyi, who the military detained on day one of the coup.

The protesters carried placards including "We want our leader", in reference to Suu Kyi, and "No dictatorship".

In Yangon's San Chaung township scores of teachers marched on the main road, waving a defiant three-finger salute that has become a signature gesture of the protesters.

"We are not worried about their warning. That's why we came out today. We cannot accept their excuse of vote fraud. We do not want any military dictatorship," teacher Thein Win Soe told AFP.

In Naypyidaw, police on Tuesday repeatedly fired water cannon against a small crowd of protesters, who withstood the barrage and refused to retreat.

"End the military dictatorship," people in the crowd yelled as the water cannon was fired.

- Military promises -

In his televised address, his first since the coup, Min Aung Hlaing insisted the seizure of power was justified because of "voter fraud".

The NLD won last November's national elections by a landslide but the military never accepted the legitimacy of the vote.

Shortly after the coup, the military announced a one-year state of emergency and promised to then hold fresh elections.

Min Aung Hlaing on Monday insisted the military would abide by its promises and reinstall democracy. He also declared that things would be "different" from the army's previous 49-year reign, which ended in 2011.

"After the tasks of the emergency period are completed, free and fair multi-party general elections will be held according to the constitution," he said.

But those pledges were accompanied by threats.

In the face of the increasingly bold wave of defiance, the military warned that opposition to the junta was unlawful.

In a statement read on state media, they said "action must be taken" against activities that threatened stability and public order.

- Global outrage -

New Zealand on Tuesday became the first foreign government to take concrete public action, announcing the suspension of high-level military and political contacts with Myanmar.

The United States has led global calls for the generals to relinquish power, and issued a fresh statement on Monday following the junta's warnings against the protesters.

"We stand with the people of Burma and support their right to assemble peacefully, including to protest peacefully in support of the democratically elected government," US State Department spokesman Ned Price said Monday, using Myanmar's former name.

Price also said US requests to speak to Suu Kyi were denied.

Pope Francis on Monday also called for the prompt release of imprisoned political leaders.

The UN Human Rights Council said it would hold a relatively rare special session on Friday to discuss the crisis.

Meanwhile relatives of an Australian economic advisor Suu Kyi say they are "distraught" over his detention in the wake of a military coup.

Macquarie University professor Sean Turnell was the first foreign national confirmed arrested by the new military junta, which took power last week.

"Myanmar is a country with which he has fallen in love, and through working on and for it for more than two decades, he brought jobs, investment, and hope to many of the poorest people there without thought of reward or concern for his own advantage," the family said in a statement.

Australian Foreign Minister Marise Payne has summoned the Myanmar ambassador over the case.