Theresa May has responded to criticism that the UK has dragged its heels on “ethnic cleansing” in Burma by announcing a ban on military training in the country.

The Ministry of Defence will “stop all defence engagement and training of the Burmese military” until it ends its security crackdown against the Muslim Rohingya minority, the Prime Minister said.

More than 310,000 people have fled to Bangladesh in recent weeks and more are trapped on the border, amid reports of extrajudicial killings and burning of entire villages.

This week, the UN’s most senior human rights official described Burma’s actions as a “textbook example” of ethnic cleansing.

Last week, Boris Johnson was criticised for describing Aung San Suu Kyi, Burma’s de facto leader and the Nobel Peace Prize-winner, as “one of the most inspiring figures of our age”, despite the violence.

And, in Canada, Ms May appeared flat-footed when Justin Trudeau, the Canadian Prime Minister, revealed he had personally spoken with Ms San Suu Kyi, to urge her to pull back.

Now the UK will end what No 10 called “educational training” of Burma’s troops, stressing the Ministry of Defence was not engaged in combat training.

Speaking at the United Nations in New York, Ms May told Sky News: “We are very concerned about what’s happening to the Rohingya people in Burma. The military action against them must stop.

“We’ve seen too many vulnerable people having to flee for their lives. Aung San Suu Kyi and the Burmese government need to make it very clear that the military action should stop.

“The British Government is announcing today that we are going to stop all defence engagement and training of the Burmese military by the Ministry of Defence until this issue is resolved.”

Downing Street was unable to provide any detail of the extent of the UK’s current level of military training in the country.

Ms May has not spoken personally with Ms San Suu Kyi, but her spokesman said Mr Johnson had done so “on a number of occasions”.

Aung San Suu Kyi publically condemns Rakhine violence

Burma’s leader on Tuesday condemned human rights violations in Rakhine state and said violators would be punished, but she did not address UN accusations of a campaign of ethnic cleansing by the military.

In her first remarks since the violent crackdown, Ms San Suu Kyi said: “Human rights violations and all other acts that impair stability and harmony and undermine the rule of law will be addressed in accordance with strict laws and justice.”

Seeking to assure foreign diplomats gathered for her speech in Naypyitaw, the capital, that those who fled to Bangladesh would be allowed to return if they passed a “verification” process, she said the government was working to restore order in the area.

Though fires have continued to flare in recent days in northern Rakhine state, she said “there have been no armed clashes and there have been no clearance operations” for the past two weeks.

Rohingya refugees – in pictures Show all 15 1 /15 Rohingya refugees – in pictures Rohingya refugees – in pictures A young girl and a baby wade through mud after arriving in Whaikhyang, Bangladesh from Burma on 10 September Dan Kitwood/Getty Images Rohingya refugees – in pictures Rohingya refugees walk through a camp in Whaikhyang, Bangladesh after arriving from Burma Dan Kitwood/Getty Images Rohingya refugees – in pictures A young Rohingya refugee gathers firewood after arriving in Whaikhyang, Bangladesh from Burma Dan Kitwood/Getty Images Rohingya refugees – in pictures Rohingya refugees wait for sacks of rice to be distributed in Whaikhyang, Bangladesh Dan Kitwood/Getty Images Rohingya refugees – in pictures Rohingya Muslim refugees arrive on a boat in Whaikhyang, Bangladesh after crossing from Burma on 8 September Dan Kitwood/Getty Images Rohingya refugees – in pictures Rohingya Muslim refugees react after being re-united with each other after arriving in Whaikhyang, Bangladesh on a boat from Burma Getty Rohingya refugees – in pictures Rohingya Muslim refugees walk along the remains of a road after arriving in Whaikhyang, Bangladesh on a boat from Burma Dan Kitwood/Getty Images Rohingya refugees – in pictures Rohingya Muslim refugees wade through water after arriving in Whaikhyang, Bangladesh by boat from Burma Dan Kitwood/Getty Images Rohingya refugees – in pictures Rohingya Muslim refugees wade through water after arriving in Whaikhyang, Bangladesh by boat from Myanmar Dan Kitwood/Getty Images Rohingya refugees – in pictures Rohingya Muslim refugees stand in the rain after arriving in Whaikhyang, Bangladesh by boat from Burma Dan Kitwood/Getty Images Rohingya refugees – in pictures Indian children hold placards and shout slogans during a protest against the alleged persecution of the Rohingya Muslims in Burma EPA/Raminder Pal Singh Rohingya refugees – in pictures Supporters of the Difa-e-Pakistan Council (DPC), an Islamic organisation, listen to their leaders' speeches against Burma's persecution of Rohingya Muslims, during a demonstration in Karachi Reuters/Akhtar Soomro Rohingya refugees – in pictures Hundreds of Iranians take part in a protest against violence in Myanmar after weekly Friday prayers, in Tehran EPA/Abedin Taherkenareh Rohingya refugees – in pictures Indonesian Muslim activists hold placards and shout slogans during a protest against the alleged persecution of the Rohingya minority in Magelang, Central Java, Indonesia EPA/Ali Lutfi Rohingya refugees – in pictures Members of an Islamic organisation shout slogans against the Burma government during a protest in Dhaka, Bangladesh EPA

“Nevertheless we are concerned to hear that numbers of Muslims are fleeing across the border to Bangladesh,” she said. “We want to understand why this exodus is happening. We would like to talk to those who have fled as well as those who have stayed.”

The latest crackdown against the Rohingya was triggered on 25 August, when an insurgent group attacked more than two dozen security sites, killing 12 people.

Militia groups, local security forces and the Burmese army responded with “clearance operations” that have forced hundreds of thousands of refugees into Bangladesh and left tens of thousands displaced inside Rakhine state.

Burma says it is targeting armed insurgents, including fighters from the Araka Rohingya Salvation Army (Arsa), which claimed responsibility for the August attacks.