Thousands of party supporters and leaders of prominent student activist groups, including the 88 Generation Peace and Open Society, turned out at the rally in Yangon.
Aung San Suu Kyi said that the current constitution needed to be amended to meet democratic norms and for elections to be free and fair.
Currently, the law says that the charter cannot be changed without more than 75% approval from the parliament. With the military holding 25 seats, its members can veto any such move and prevent Aung San Suu Kyi from becoming president because her sons are British nationals.
An article in the constitution says anyone whose spouse or children owes allegiance to a foreign power cannot become president or vice president.
The Nobel Peace Prize laureate has been holding rallies to gain public support and to persuade the military and the government to change their opposition to amending the constitution.
Several other provisions are also under scrutiny for revision, and some proposed changes would strengthen self-government in regions of the country dominated by ethnic minorities.
Aung San Suu Kyi's National League for Democracy party boycotted the 2010 election, but successfully contested byelections in 2012 after electoral reforms were implemented, with the Nobel laureate herself winning a seat in the lower house.