Britain has sanctioned members of Myanmar's military and some of its business interests in wake of the coup, and has demanded the restoration of democracy.
But Beijing - the top ally of Myanmar's military - has voiced growing concern about instability, and has said it is speaking to "all parties".
At least 614 protesters and bystanders have been killed by security forces through Thursday, according to the Assistance Association for Political Prisoners, which monitors casualties and arrests.
State television channel MRTV reported Friday night that a military court had sentenced to death 19 people - 17 in absentia - for allegedly killing an army officer in Yangon on March 27.
Kyaw Zwar Minn said he was in contact with the British Foreign Office, and Whitehall sources confirmed the Government was speaking with the Myanmar regime.
"I say categorically, we can not - we simply can not - allow the military to destabilize the region once again through its unrelenting campaign of violence, their campaign of repression, and especially - especially - against the backdrop of an unprecedented global pandemic", Linda Thomas-Greenfield said.
Scotland Yard said in a statement: 'We are aware of a protest outside the Myanmar embassy in Mayfair, London. "Violence never leads to peaceful sustainable solutions".
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"Your collective, strong action is needed immediately", Ambassador Kyaw Moe Tun told the UN Security Council meeting on Friday.
More than 600 people have been killed by security forces cracking down on protests against the February 1 coup in which the military ousted the elected government of Aung San Suu Kyi.
United Nations special envoy for Myanmar, Christine Schraner Burgener, arrived in Bangkok on Friday on a mission to resolve the crisis in Myanmar, although she has been denied permission to visit the country.
"At one end, there are Thailand, Laos and Cambodia, who are in the mode of 'back off, there's nothing to see, it's a question of internal politics, '" one diplomat said, while Singapore, Malaysia and Indonesia are open to a more active role for Asean. He also accused members of deposed leader Aung San Suu Kyi's National League for Democracy of arson and said the protest campaign was being financed by foreign money, but he gave no details.
"We are cooperating with foreign countries and working together with neighbouring countries", the spokesman said.
Local media reports said the fighting continued during the day, and the death toll could be higher.
The military has retaliated with air strikes in KNU's territory, which the rebel group says has displaced more than 10,000 civilians in Karen state.
The protest movement has sought to disrupt the military's ability to run the country by encouraging key public workers such as doctors and railway staff to stay at home.