Karen Pierce called on Tuesday for the "root causes" of the crisis — which has seen hundreds of thousands of Rohingya flee Myanmar for neighboring Bangladesh as a result of what the UN has described as a "textbook example of ethnic cleansing" — to be addressed, aljazeera.com reported.
"In order to have accountability there must be a proper investigation," said Pierce, who is on a four-day UN Security Council (UNSC) visit to Myanmar and Bangladesh.
"It doesn't matter whether it is international or domestic, as long as it's credible," she said.
The probe could be carried out either by the International Criminal Court or Myanmar's own government, Pierce added.
But some questioned the envoys' commitment to justice.
"Accountability of the perpetrators is the most important step, but unfortunately the UN Security Council seems unwilling to apply this to the Burmese military's top brass," Kyaw Win, founder of the Burma Human Rights Network, told Al Jazeera.
"Failure of accountability has sent the wrong signals to the perpetrators and now they know that they can get away with it [their actions]. Inaction or ineffective action from the international community risks many lives in Burma," he said, using Myanmar's former name.
Some 670,000 Rohingya have fled Myanmar since security forces launched a violent crackdown in the country's western Rakhine state last August, according to the UN, in the wake of deadly attacks on military posts blamed on the Rohingya.
Since then, Myanmar security forces have been accused of rape, murder, torture and setting Rohingya homes on fire.
'Stronger action' on sexual violence
Government officials have denied the military's complicity in instigating violence against the Rohingya, though pledged on Tuesday to take "harsh" action against any perpetrators of sexual violence.
Min Aung Hlaing, commander-in-chief of the Myanmar Armed Forces, told the Global New Light newspaper on Tuesday the military was "taking stronger actions against such offenders".
"Sexual violence is considered despicable ... according to the tradition, culture and religion of the country," Hlaing said, adding that the government is ready to receive any refugees who wish to return to Myanmar.
De facto leader Aung San Suu Kyi, in her nearly hour-long meeting with the envoys, pledged to investigate any credible accusations of abuse, said diplomats who attended.
Suu Kyi noted Myanmar's difficulties in transitioning to rule of law after decades of military dictatorship, said the diplomats, speaking on condition of anonymity.
"She said what had happened or what was alleged to have happened to some of the Rohingya villagers was not acceptable and that if evidence were available it should be reported to the Burmese authorities and they would investigate," said Pierce.
Suu Kyi's civilian government has little control over the military.
In February, Bangladesh released a list of more than 8,000 Rohingya for repatriation. As of April 1, not a single person had been returned, despite Myanmar officials having verified the identities of some 600 individuals, according to international rights group Human Rights Watch.
The UN's refugee agency has said conditions in Myanmar are "not yet conducive for returns to be safe, dignified and sustainable".
Myanmar and Bangladesh announced a repatriation deal in January, but rights groups and Rohingya have raised concerns about the agreement, saying it does not guarantee full citizenship or safety for those who return.