Mr Zardari's remarks have caused controversy
Pakistan's top diplomat in London says Pakistan is opposed to outside militants engaging in "cross-border terrorism" in Kashmir.
But High Commissioner Wajid Shamsul Hasan says that Kashmiris themselves are justified in using force to drive India out of Kashmir.
He was seeking to clarify a Wall Street Journal report at the weekend.
The newspaper quoted President Asif Zardari as calling Islamic militants in Kashmir "terrorists".
The report caused outrage among Kashmiri Muslims opposed to Indian rule, many of whom who regard militant groups fighting Indian rule as freedom fighters.
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, and burnt an effigy of Mr Zardari.
Leading Kashmiri separatists denounced him for being "afraid of India".
'Damaged the cause'
High Commissioner Hasan said that Mr Zardari was not seeking to undermine "the indigenous struggle by the Kashmiri people for the right of self-determination" in his Wall Street Journal interview.
Troops enforce a curfew in Srinagar to prevent anti-India protests
Mr Hasan made his comments in an e-mail sent to various media including the BBC. He said that Mr Zardari had repeated that "Pakistan is opposed to external militants indulging in cross-border terrorism and subverting a genuine indigenous freedom movement".
Correspondents say the phrase "cross-border terrorism" is one that has been used consistently by India, which has accused Pakistan of arming and helping Pakistani-based militants fighting in Kashmir.
The e-mail also said that Mr Hasan believed that "such foreign militants as a matter of fact have damaged the Kashmiri cause rather than helping their just struggle for freedom".
The first armed groups fighting Indian rule in Kashmir sprang up in the 1980s and were made up of Kashmiris. Later Pakistani militants came to play the dominant role there.
The BBC News website asked Mr Hasan if Pakistan's position was that indigenous militants were justified in using force against Indian forces in Kashmir, to which he replied, "Yes".
Pakistan has fought two wars with India over Kashmir and both countries claim the territory as its own.
India maintains a huge security presence in Kashmir and the military and police, as well as the militants, have frequently been accused of gross human rights abuses.
On Monday Pakistan Information Minister Sherry Rehman of Mr Zardari's Pakistan People's Party (PPP) sought to clarify Mr Zardari's comments.
Kashmir separatists like Syed Ali Shah Geelani say 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.
The Wall Street Journal also quoted Mr Zardari as making a series of conciliatory comments about nuclear rival India. "India has never been a threat to Pakistan," he said and "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."
High Commissioner Hasan said such comments did not prejudice in any way UN resolutions on Kashmir which call for a plebiscite in Kashmir to determine its future.