"We don't agree with what Prashant Bhushan said about Kashmir, it's his personal view," said party chief and Delhi Chief Minister Arvind Kejriwal. "Whatever the army wants to do regarding deployment, there is no question of a referendum on it. We do not support Prashant Bhushan's statement."
The party later read out a clarification on behalf of Mr Bhushan: "AAP is of the view that Kashmir is an integral part of India. I share this view."
Mr Bhushan had earlier said on NDTV's "We The People" that in keeping with participatory democracy, locals in the Kashmir Valley should be allowed to determine whether they want the army for internal security or not. "It is very important to take the wishes of the people into consideration about their own security," he said.
The AAP leader said the government should decide if the army should deal with external threats along the border.
The comments were criticised across the spectrum. The Congress, which gives external support to the AAP in Delhi, accused the year-old party of making irresponsible statements.
Senior BJP leader Arun Jaitley said in a blog, "Issues of national security cannot be decided by populism or referendum. They can only be decided on security considerations." (Read Arun Jaitley's blog)
Mr Jaitley followed it up with a scathing tweet, "Ideology of AAP as revealed post-elections - it stands for nationalization, weak National security and high subsidies and higher taxation."
Jammu and Kashmir Chief Minister Omar Abdullah also tweeted his disapproval, saying, "Governments get a mandate to govern and decide, they don't need to conduct a referendum before every tricky decision. Leaders must lead."
In Kashmir's decades-long battle against militancy, the army has often faced allegations of misusing the Armed Forces Special Powers Act (AFSPA) which gives it sweeping powers to interrogate and arrest civilians in conflict regions.