Mr Zardari's remarks mark a radical break with the past
A group of Muslim protesters in Indian-administered Kashmir has defied a curfew to denounce Pakistani President Asif Zardari and burn his effigy.
Mr Zardari has provoked outrage after being reported as saying that Islamic militants fighting Indian rule in Kashmir were "terrorists".
Leading Kashmir separatists have also denounced Mr Zardari.
Pakistan has supported anti-Indian militants and fought two wars with India over Kashmir.
Many Kashmiris and Pakistanis regard militant groups fighting Indian rule in Kashmir as freedom fighters. Mr Zardari made his controversial reference to them as "terrorists" in an interview with the Wall Street Journal.
Protesters took to the streets of the town of Baramullah on Monday, close to the Line of Control that separates Indian and Pakistan-administered Kashmir, despite a curfew imposed by Indian security forces in Muslim-majority areas of the Kashmir Valley.
The BBC's Altaf Hussain in Srinagar says it is the first time that a Pakistani leader's effigy has been burnt in Indian-administered Kashmir where anti-India protests have often been marked by pro-Pakistan slogans.
Prominent politicians fighting for an end to Indian rule in Kashmir joined in the condemnation of Mr Zardari. Syed Ali Shah Geelani told the BBC that "Zardari has made these remarks to please the Americans".
"Zardari fears India and would do anything to please that country even at the cost of Pakistan's dignity," Mr Geelani said. "Kashmiri youths have been fighting for a just cause."
India maintains a huge security presence in Kashmir and the military and police, as well as the militants, have frequently been accused of human rights abuses.
"In reality," Mr Gilani said, "the people of Kashmir have been victims of state terrorism."
In Pakistan itself, Information Minister Sherry Rehman of Mr Zardari's Pakistan People's Party (PPP) sought to clarify Mr Zardari's comments.
Mr Gilani said Mr Zardari 'fears India'
"The president has made it very clear that the just cause of Kashmir and its struggle for self-determination has been a consistent central position of the PPP for 40 years now," she told the BBC Urdu service.
"There is no change in that policy. He has never called the legitimate aspirations of Kashmiris an expression of terrorism, nor has he undermined the sufferings of the Kashmiri people."
However she offered no explicit support for the use of violence to oust Indian forces from Kashmir.
Pakistan and India have fought three fully-fledged wars since independence in 1947. They came close to another war in 2002 after militants stormed the Indian parliament in Delhi in December, 2001.
The BBC's Barbara Plett in Islamabad says Pakistan's powerful military has long-defined India as a threat to Pakistan's existence and in the past it has given covert backing to the militants in Kashmir.
But Mr Zardari told the Wall Street Journal that "India has never been a threat to Pakistan" and that "I, for one, and our democratic government is not scared of Indian influence abroad."
He also said that Pakistan had to develop strong economic ties with India. "There is no other economic survival for nations like us. We have to trade with our neighbours first."
He also appeared to acknowledge that his government had given consent to US air strikes in Pakistan.
Pakistan and India took part in a faltering peace process under the former President Pervez Musharraf.
But suspicions always ran deep, and relations have soured recently.
Our Islamabad correspondent says Mr Zardari's comments mark a radical break with the past.
More reaction is expected in Pakistan after the country returns to normal working following the Eid festival holiday.