"We met for about one hour. We discussed the release of Daw Aung San Suu Kyi and the political prisoners," Tin Oo told reporters following Thursday's meeting with Quintana.
"We also spoke of our request for a meeting between the Senior General [Than Shwe] and Daw Aung San Suu Kyi, and for a meeting between [her] and our central committee members so that we can continue our work for the future."
Daw is a term of respect in Myanmar.
|Quintana has asked the military for a meeting with Aung San Suu Kyi [Reuters]
Aung San Suu Kyi wrote in November to Than Shwe, the head of Myanmar's ruling military, to request a meeting with him. They last met in 2002.
Quintana told the NLD members that he had asked to meet Aung San Suu Kyi but had had no answer yet from the government, Tin Oo said.
On the upcoming elections, expected to be held later this year, Tin Oo said the NLD would stick to earlier calls for a review of the country's constitution, introduced in 2008.
The new national charter was brought in after a referendum that was held days after Cyclone Nargis hit the country, killing an estimated 138,000 people.
The constitution prohibits Aung San Suu Kyi from standing in elections and reserves a quarter of parliamentary seats for the military.
Myanmar's generals have not yet set a date for the polls, fuelling speculation from the opposition and human rights group that they are a facade designed to legitimise the military's hold on power.
In 1990, the NLD won by a landslide in the country's national elections but the military refused to recognise the result and prevented them from taking power.
Aung San Suu Kyi has been detained for most of the last two decades and her house arrest was extended by 18 months in August after an incident in which an American man swam to her lakeside home.
The extension effectively ruled her out of the polls and sparked global outrage.