Myanmar's Aung San Suu Kyi is facing mounting international pressure for her handling of violence in Rakhine state and the Rohingya refugee crisis.
In a speech on Tuesday, the de facto leader condemned rights abuses but did not blame the army nor address allegations of ethnic cleansing.
Leaders and diplomats from several countries have since expressed strong disappointment with her stance.
More than 400,000 Rohingya have fled to Bangladesh since late August.
The latest unrest in troubled Rakhine was sparked by deadly attacks on police stations across the state last month, blamed on a newly emerged militant group, the Arakan Rohingya Salvation Army (Arsa).
In a phone call, US Secretary of State Rex Tillerson told Ms Suu Kyi that he welcomed her statement that refugees would be able to return once verified.
But he urged her to facilitate humanitarian aid and "address deeply troubling allegations of human rights abuses and violations", the State Department said.
Speaking to the UN Assembly, French President Emmanuel Macron said "the military operation must stop, humanitarian access must be guaranteed and the rule of law restored in the face of what we know is ethnic cleansing".
He also said he would start a Security Council initiative to ensure humanitarian access and an end to the violence.
UN Secretary General Antonio Guterres also urged Myanmar to "end the military operations" and "address the grievances of the Rohingya, whose status has been left unresolved for far too long".
Turkish President Recep Tayyip Erdogan called on the international community to act on the crisis warning that "unless the tragedy taking place in Myanmar is brought to a halt, humanity will have to live with the shame of another dark stain in its history".
A spokesperson for the EU said Ms Suu Kyi's invitation for international diplomats to visit the affected areas - previously ruled out of bounds by the government - was "a step forward".
But he said Myanmar's leadership needed to show "that the democracy they fought so hard for can work for all the people of Myanmar, beyond ethnic, social and religious boundaries".
UK Prime Minister Theresa May also said the military action in Rakhine had to stop. The UK is suspending training courses for the Myanmar military in light of the violence.
Amnesty International said Aung San Suu Kyi's speech was "little more than a mix of untruths and victim blaming," and accused her of "burying her head in the sand" by ignoring the abuses by the army.
Having led Myanmar's struggle out of decades of military dictatorship, Ms Suu Kyi received the Nobel Peace in 1990. She remains overwhelmingly popular in the country.