Myanmar says it will allow Paulo Sergio Pinheiro, a human rights investigator, to visit the country after barring him four years ago.
A spokeswoman for Ban Ki-moon, the UN secretary-general, said on Monday that the Myanmar foreign minister had sent a letter to Ban suggesting that Pinheiro visit before an Asean meeting in November.
Myanmar is a member of the Southeast Asian Nations (Asean) which will hold a regional summit on November 17.
The 10-member group had expressed "revulsion" at the violent repression of pro-democracy demonstrations in recent weeks.
"Where are the peace and human rights defenders of the world (the super powers)? They haven't done enough in this case. Isn't there oil in Myanmar?"
Lost Soldier, Arusha, Tanzania
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It asked Myanmar's military government to exercise restraint and seek a political solution to the street protests sparked by price rises.
Pinheiro was appointed as the UN's independent expert on human rights in Myanmar seven years ago.
The UN Human Rights Council at an emergency session in Geneva early this month condemned the crackdown on protesters, calling for an immediate investigation.
Doru-Romulus Costea, who chairs the council, appealed at the session for an urgent visit by Pinheiro saying he would be able to travel "at any time should the government of Myanmar give its approval".
The council passed a resolution - the first to criticise a government other than Israel - deploring "continued violent repression of peaceful demonstrators in Myanmar, including through beatings, killings, arbitrary detentions and enforced disappearances".
The Myanmar government violently reacted to public protests that were initially sparked by a sharp hike in fuel prices in August, which later turned into anti-government rallies led by Buddhist monks - the biggest in nearly 20 years.
However, Ibrahim Gambari, Ban's special envoy to Myanmar, is unlikely to return before mid-November as planned because Myanmar has not given him a visa for an earlier visit.
Gambari is currently in India as part of a six-nation tour of Asia aimed at increasing the pressure on Myanmar's generals.
On Monday, Zalmay Khalilzad, the US ambassador to the UN, said Gambari was needed in Myanmar to facilitate the necessary negotiations between the government and the opposition led by detained pro-democracy leader Aung San Suu Kyi.
"We are calling on all those with influence to redouble their efforts to get Mr Gambari there as quickly as possible."