"The perpetrators of the unlawful coup against the democratic government of Myanmar have no authority to countermand the legitimate authority of the President of my country," Ambassador Kyaw Moe Tun wrote in his letter to the UN.

But the Myanmar foreign ministry is backing a deputy ambassador to take control of the country's UN representation, according to UN spokesman Stephane Dujarric.

"It's a unique situation we have not seen in a long time," Dujarric told reporters on Tuesday of the dueling claims. He added that the UN is "trying to resolve things as quickly as possible."

"We need further strongest possible action from the international community to immediately end the military coup, to stop oppressing the innocent people, to return the state power to the people and to restore the democracy," he told the UN on Friday.

Kyaw Moe Tun said he was delivering the speech on behalf of Suu Kyi's government, and flashed the three fingered "Hunger Games" salute used by protestors on the streets of Myanmar, prompting a rare round of applause from his UN colleagues at the end.

The new US ambassador to the UN, Linda Thomas-Greenfield, praised the envoy's "courageous" remarks.

'A unique situation'

Both men already have UN credentials to enter the building, raising an obvious practical question: Who is entitled to the seat in the General Assembly where Myanmar sits?

In past such diplomatic tussles, if the fight raged on, a committee of the UN would determine who get the proper "credentials" to represent their country.

However such a process could also widen the crisis and take time. The UN spokesman has said that UN Secretary-General Antonio Guterres wants the Security Council to get Myanmar's military rulers to return the country to democracy.

On Tuesday, US State Department spokesperson Ned Price said that "when it comes to Kyaw Moe Tun, we understand the permanent representative remains in his position."

"We will continue to opposed the military coup, and we will continue to support the restoration of Burma's democratically elected civilian government going forward," Price added.

"I say 'attempted,' since the takeover has not stabilized, it would appear to be roundly rejected by the people. It is important the international community does not lend legitimacy or recognition to this regime," she said.

The UK has proposed a meeting of the UN Security Council to discuss Myanmar on Friday, a diplomat tells CNN. Such a session would likely begin behind closed doors.

The Council has expressed concern over developments such as the military takeover but has not condemned the military leaders.