(Rewrites with Myanmar )
By David Brunnstrom and John Irish
NEW YORK, Sept 18 (Reuters) - Britain, France and Australia urged Myanmar leader Aung San Suu Kyi on Monday to push for an end to military violence against Rohingya Muslims, while her national security adviser said those who had fled could return but the process had to be discussed.
The military response to insurgent attacks last month in the western region of Myanmar sent more than 410,000 Rohingya Muslims fleeing to neighboring Bangladesh, escaping what the United Nations has branded as ethnic cleansing. government says about 400 people have been killed in the fighting.
"We will make sure that everybody who left their home can return to their home but this is a process we have to discuss," Myanmar national security adviser Thaung Tun told Reuters on Monday after a ministerial meeting on the crisis hosted by Britain on the sidelines of the United Nations General Assembly.
"We want to make sure that everybody who needs humanitarian assistance gets it, without discrimination. That is one of the things we agreed on," he said.
Nobel laureate Suu Kyi has faced a barrage of criticism from abroad for not stopping the violence. She is due to speak to the nation on Tuesday about the crisis, which the United States has described as a "defining moment" for Myanmar.
"We expect from Mrs Aung Sang Suu Kyi tomorrow a strong statement in this direction," French Foreign Minister Jean-Yves le Drian told reporters in New York.
British Foreign Secretary Boris Johnson hosted a ministerial meeting to discuss ways to resolve the Rohingya crisis, which included ministers from Turkey, Australia, Indonesia, Sweden and U.S. Ambassador to the United Nations Nikki Haley.
"What we are trying to get everyone to agree is that, number one, the killings have got to stop, and the violence has got to stop. And we look not just to the military but also to Daw Suu to show a lead on that," Johnson said before the meeting.
China, which, like the United States has worked to forge closer ties with Myanmar, a strategically important country in Southeast Asia, will not attend, a Chinese spokesman said, citing "a really packed calendar" for Foreign Minister Wang Yi.
Turkish Foreign Minister Mevlut Cavusoglu told Reuters ahead of the British meeting that a lasting political solution needed to be found for the Rohingya in Myanmar.
'ENORMOUS TRAGEDY'
About a million Rohingya lived in Rakhine State until the recent violence. Most face draconian travel restrictions and are denied citizenship in a country where many Buddhists regard them as illegal immigrants from Bangladesh.
Australian Foreign Minister Julie Bishop said she wanted to hear Suu Kyi offer a solution "to what is a tragedy of enormous proportions." She said that during the ministerial meeting in New York there "was unanimity in the view that the violence must end and that there be a ceasefire.
"And we emphasized the need for humanitarian support to get through and also that the Rohingya must be able to return home," Bishop said.
Haley said the meeting simply went "very well."
Washington has called for the protection of civilians, and a deputy assistant secretary of state, Patrick Murphy, is due in Myanmar this week.
U.S.-Myanmar ties improved after the military began withdrawing from government in 2011, and paved the way for a 2015 election won by Suu Kyi's party. But the military retains a strong hand in government and remains responsible for security.
A Trump administration official told Reuters last week the violence made it harder to build warmer ties with Myanmar, and there would likely be some "easing" in the short term, but he did not expect a return to sanctions.
For years, the United States and Western allies imposed sanctions on Myanmar in support of Suu Kyi's campaign for democracy. Myanmar's response was to forge closer ties with China.
Human Rights Watch U.N. director Louis Charbonneau called for "strong U.N. action to compel Myanmar security services to end their ethnic cleansing campaign."
"With so many influential leaders gathered in New York, the next step should be work on a U.N. General Assembly resolution condemning the abuses and a Security Council resolution to impose targeted sanctions and an arms embargo on the commanders leading this brutal campaign" he said.
However, Myanmar earlier this month it was negotiating with China and Russia, both permanent veto wielding members of the Security Council, to block any bid to censure the country over the violence. (Writing by Michelle Nichols; Editing by Bernadette Baum and Grant McCool)