Aung San Suu Kyi was detained for 15 years between 1989 and 2010 and released last year.
This year she and others of the National League for Democracy were elected to Parliament and she is now Leader of the Opposition.
But she is not entitled to stand for president at the next elections in 2015.
The constitution was amended in 2008 to prevent anyone with a spouse or children who are foreign citizens from becoming president.
Her husband has died but her children are British.
"I do make a point of saying that we need to make certain that the road to democracy is going in the right way and that a commitment to a genuine transition to democracy will depend on whether there is a genuine commitment to necessary amendment to the constitution."
Asked what New Zealand could do she said: "New Zealand should really insist that if Burma is to be a genuine democracy and the 2015 elections are to be fair as well as free, then these necessary amendments will have to be moved."
She said the commitment of the present Burmese Government to constitutional changes would indicate how committed it was to democratisation.
As well as denying her a run at the top job, the constitution reserves a quarter of all seats in both houses and three ministerial roles - including defence minister - for the military.
Mr Key did not raise constitutional issues with Mr Sein yesterday but said he would raise it when he visits New Zealand next month.
Mr Key is one of several leaders who have recognised steps to democracy with Thein Sein by visiting the country.
Asked if it was too early for such visits, Aung San Suu Kyi said: "I don't think one can say anything is too early or too late. I depends what you make of it and you've got to make the best of whatever happens.
"There is of course a danger that it will give rise to a perception that things are going very well in Burma."
That had to be counteracted by saying things were not yet as they should be "but everybody is trying to make sure they go the right way".
She said the outside world needed to be careful about how it supported Burma.
"The kind of support that comes to us should be the kind of support that empowers the people, rather than to empower the Government.
"What we want is people-centred aid rather than Government centred help."
She cited support for local government.
"For a genuine democracy to emerge in this country, you need to strengthen the regions rather than strengthen the centre."
New Zealand has changed its official position and recognised Burma as Myanmar.
She said she did not support the name Myanmar because it was imposed on the country.
"One day suddenly in the state newspapers it as announced that henceforth this county was going to be known as Myanmar."
She had explained her views to Mr Key but added: "As somebody who believes in democracy, I think you have the right to decide what you call it."
She has a special place for New Zealand in her heart because in her gloomiest moments in house arrest she would think about living in New Zealand or Canada.
"I thought perhaps in those places they were unpolluted areas and of course I have always thought New Zealand was rather romantic - the land of the long cloud and so on - not to mention the kiwifruit.
Mr Key presented her with an ornately carved greenstone pendant which was commissioned from Colin Davidson of Ngai Tahu, and a box of kiwifruit.
Asked if Burma had a free press, she said all three newspapers were state owned and there was "something lacking in media freedom".
