The UN envoy to Burma, Ibrahim Gambari, has made progress in promoting dialogue between the military rulers and the opposition, the organisation has said.
Ms Suu Kyi met Mr Gambari just before he left Rangoon
Mr Gambari has just completed a six-day visit to Burma, during which he met a number of ministers as well as detained pro-democracy leader Aung San Suu Kyi.
The UN said a path to "substantive dialogue" was now under way.
The comments come despite signs that Mr Gambari's visit has made little headway in pushing the junta towards reform.
This is Mr Gambari's second visit since the military violently suppressed anti-government protests in September.
Burma's ruling generals are under huge pressure to make definite democratic changes in the wake of the crackdown.
"We now have a process going which would lead to substantive dialogue" between the government and Aung San Suu Kyi, the UN statement said.
"The sooner such a dialogue can start, the better for Myanmar [Burma]."
The statement also confirmed that Mr Gambari had been invited to return to Burma in the next few weeks.
Ms Suu Kyi has been held under house arrest for years
It added that Ms Suu Kyi had authorised Mr Gambari to make a statement on her behalf, though it did not say when he would do so.
While there is little information so far about the content of Mr Gambari's meetings, analysts say it is unlikely that the visit marks a real step forward.
It appears he was not given access to junta head General Than Shwe, and Burma's state media reported early on Thursday that the generals had rejected Mr Gambari's proposal to mediate in talks between the regime and Ms Suu Kyi.
Ms Suu Kyi was driven from her home in the main city of Rangoon, where she is being held under house arrest, to meet Mr Gambari at a nearby government guest house on Thursday.
After an hour she was reportedly driven away, and Mr Gambari headed for the airport, drawing his latest visit to a close.
The envoy arrived in Burma on Saturday and the UN said he had held "open and detailed discussions" with Prime Minister Thein Sein.
"While taking note of the views of the Myanmar [Burma] government, Mr Gambari stressed that a return to the status quo before the crisis would not be sustainable," the UN said in an earlier statement.
But there was no mention in the statement of a meeting with Gen Than Shwe. The UN said only that Mr Gambari had delivered a letter for the junta head.
Widespread protests broke out across Burma during September. In response, the military regime detained at least 3,000 people and opened fire on crowds, with dozens feared dead.
On Wednesday, the Burmese authorities said all but 91 of those detained in the aftermath of the protests had now been freed.
Human rights groups say at least 600 people are still in jail.