Myanmar's government is investigating a speech by a Buddhist monk in which he called a UN rapporteur a "whore".
South Korean rapporteur Yanghee Lee was in Myanmar last week to highlight the plight of its Muslim minority.
But at a protest against the visit, monk Ashin Wirathu told Ms Lee she should have sex with Muslim Rohingya minority if she liked them so much.
The monk is a Buddhist nationalist who spent almost a decade in jail for inciting anti-Muslim violence.
Buddhist nationalism, largely led by monks including Wirathu, has been energised since the end of military rule in 2011.
In 2012, scores of people died and thousands were left homeless after violence broke out between Buddhists and Muslims in Rakhine state, mostly from the Rohingya minority. Violence has flared several times since then.
The UN says the Rohingya are being persecuted, and last week passed a resolution calling on Myanmar (also known as Burma) to give them citizenship.
But the Myanmar government views the Rohingya as foreign migrants, and there is widespread public hostility towards them.
During her visit, Ms Lee said Myanmar was in danger of slipping backwards in its transition to democracy since the end of military rule in 2011.
She criticised proposed laws on race and religion which would among other things impose state regulations on religious conversions and restrict interfaith marriages. Activists say they would disproportionately affect Muslims.
She said many people were still living in "abysmal conditions" in camps in Rakhine state after the 2012 violence, and that "collective punishment" of all Muslims in the state for the deeds of a few in the unrest was "not the answer".
In a speech at the rally against Ms Lee on Friday - which was widely shared online - Wirathu said Ms Lee should have sex with the Rohingya if she liked them so much.
"Don't assume you are a respectable person, just because you have a position in the UN," he said. "In our country, you are just a whore."
He later defended his comments, telling the AFP news agency: "If I could find a harsher word, I would have used it. It is nothing compared to what she did to our country."
Wirathu was jailed in 2003 for inciting anti-Muslim violence but was released in 2012 as part of a prisoner amnesty.
He is a leader of the 969 movement, which says Myanmar should remain a Buddhist country and calls for restrictions and boycotts on Muslims.
Information Minister Ye Htut said on his Facebook page on Wednesday that he had asked the ministry of religious affairs to investigate the monk's comments.
He added that he believed religious leaders should recite speeches reflecting love, compassion, empathy and good ethics.
But the BBC's Jonah Fisher in Yangon says criticism of the comments has been muted because no politicians want the powerful monks to turn on them.