The statement said that Gambari may return to Myanmar in a few weeks to continue efforts towards reconciliation between the military government and the opposition.
Suu Kyi will meet officials from her party and a senior military government official on Friday, state television reported after the UN issued its statement.
She has not been allowed to meet with NLD members since May 2004, but it will be her second meeting with Aung Kyi, Myanmar's labour minister, since he was appointed by in late October to liaise with the opposition.
Gambari met Suu Kyi for an hour on Thursday as part of his second mission to the country since the military government violently put down pro-democracy demonstrations in September.
"Until the generals' military hardware is crumbled, they won't listen to anyone"
Oomlwin, Yangon, Myanmar
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Suu Kyi, who leads the National League for Democracy (NLD), was granted permission to leave her home, where she has been held under house arrest, to meet the UN envoy.
Gambari also met other NLD members in the capital Naypyidaw, 400km north of Yangon, before meeting Suu Kyi, officials said.
On Wednesday, Gambari met senior generals, including Thein Sein, Myanmar's prime minister, in Naypyidaw.
The UN envoy was unable to meet Than Shwe, who is Myanmar's most senior leader, during his six-day mission.
The military government also rejected suggestions for a tripartite meeting involving Suu Kyi, a government member and Gambari.
On Wednesday, state media reported the government had rejected Gambari's request for the three-way talks.
Brigadier-General Kyaw Hsan, the information minister, told Gambari that Myanmar's generals would not support outside "interference".
Kyaw Hsan said "currently the tripartite meeting will not be possible", the New Light of Myanmar daily reported on Wednesday.
Gambari's second visit to Myanmar in a month is an attempt to pressure Myanmar's military government to adopt democratic reforms.
The government violently put down widespread pro-democracy protests in September, which were led by Buddhist monks.
The UN said in a statement late on Wednesday that Gambari gave Thein Sein a letter from Ban Ki-moon, the UN secretary-general, to pass on to Than Shwe.
In comments published in the New Light of Myanmar, Kyaw Hsan said the government would not be pressed into making democratic reforms.
"If you wish to see democracy flourishing in Myanmar, you should try to persuade other nations to co-operate with us in assisting [with] the task," he said.
|Buddhist monks led popular pro-democracy |
protests in Myanmar in September [AFP]
"Here, what we would like to say is that we will welcome positive co-ordination and co-operation for Myanmar affairs, but will never accept any interference that may harm our sovereignty."
State media has indicated the government is only willing to adopt its own seven-stage "road map to democracy".
The plan has been criticised by Western governments as a method to keep the military generals in power.
Gambari appealed on Wednesday for restrictions on Suu Kyi and all political prisoners to end, the UN and Kyaw Hsan said.
However, Myanmar's rulers say that Suu Kyi must first abandon her support for international sanctions against the government.
Suu Kyi led the NLD to victory in a general election in 1990, but Myanmar's generals have not allowed her party to take office.