UN Secretary General Ban Ki-moon has asked the Burmese leader to free Aung San Suu Kyi and to allow him to visit the Nobel peace laureate.
Mr Ban said General Than Shwe had not yet granted him permission to see the 64-year-old opposition leader.
However, he added that he awaited a final reply before his two-day mission ends tomorrow.
Mr Ban arrived in Burma, officially known as Myanmar, this morning. He flew into the new capital city of Naypyidaw, the remote stronghold of General Than Shwe.
Earlier, a prison court had again adjourned the widely condemned trial of Ms Suu Kyi on charges of breaching the terms of her house arrest.
After the meeting Mr Ban said: 'I told him that I wanted to meet her in person.
'He told me that she is on trial but I told him this is my proposal, this is important and I am waiting for their consideration and reply.'
General Than Shwe appeared in his olive green military uniform at the start of the meeting but did not speak.
Asked how soon he expected a response from the junta on his request to see her, Mr Ban said with a smile: 'I am leaving tomorrow, so logically speaking I am waiting for a reply before my departure.'
The UN chief said he had also sought the release of the more than 2,000 political prisoners that the UN says are held in Burma ahead of elections promised by the ruling generals in 2010.
'I proposed and I urged that all political prisoners should be released before this election begins, so that this election can be all inclusive,' Ban said.
Ms Suu Kyi was transferred from house arrest to prison in May on charges of violating her house arrest, after an American man swam uninvited to her lakeside house.
She has spent most of the past two decades in detention and now faces five years imprisonment if convicted.
