Around 250,000 turn out in two cities in support of a bid to join the UN.
The island has been trying for years to rejoin but China has so far managed to block its application.
Taiwan‘s more aggressive approach this year has heightened tensions with China and Beijing has vowed to use force against Taiwan if it ever declares independence.
‘Not legally possible’
Ban said on Tuesday that Taiwan‘s application to join the UN was not accepted for legal reasons because of a 1971 UN resolution that gave China‘s seat to China.
Beijing regards Taiwan as part of its territory, and says it will use force if it declares independence.
Beijing and Taipei both claim they are the legitimate government of all China.
Taiwan has been a multi-party democracy since 1996.
Taiwan’s defence ministry says China now has nearly 1,000 missiles aimed at the island.
The US is Taiwan’s major arms supplier and has warned China that any attack would be viewed with “grave concern”.
The Marshall Islands, representing that group, asked for Taiwan’s application to be considered by a new general assembly session.
That request will be considered on Wednesday by a key general assembly committee.
Despite this, Chen Shui-bian, Taiwan’s president, is planning to hold a referendum on UN membership alongside presidential elections in March, just months before Beijing hosts the Olympics.
Mark Seddon, Al Jazeera’s correspondent at the UN, said the Chinese would take a hard line on Taiwan but were unlikely to launch military action.
He said that while China has been increasing the number of missiles aimed at Taiwan, actually going to war was another matter.