He was speaking after talks in London with UK Prime Minister Gordon Brown, who pledged £12m ($18m) in humanitarian aid for north-west Pakistan.
Mr Zardari said the two countries were united in fighting the threat to their countries' democratic way of life, and also repeated assurances that his country's arsenal was in safe hands.
There was an international outcry recently when the militants moved into Buner district, just 100km (67 miles) from Islamabad.
Pakistan has continued its military offensive to regain control of the region, and has reported the deaths of 11 militants in the Swat valley in the past 24 hours.
Residents trapped in Mingora, the main town in Swat, told AFP news agency by telephone that militants had planted mines and were digging trenches.
"People are becoming mentally ill, our senses have shut down, children and woman are crying, please tell the government to pull us out of here," said one shopkeeper, who did not want to give his name.
"Forget the lack of electricity and other problems, the Taleban are everywhere and heavy exchanges of fire are routine at night."
The report the BBC map was based on covered the 24 districts of NWFP and the seven tribal agencies and six frontier regions of the Federally Administered Tribal Areas (FATA).
Pakistan's president tells the BBC's David Loyn that the survey is 'incorrect'
The researchers analysed reports from BBC Urdu correspondents over the past 18 months, backed up by conversations with local officials, police officers and journalists.
They concluded that in 24% of the region, the civilian government no longer had authority and Taleban commanders had taken over administrative controls.
Either the Taleban were in complete control or the military were engaged in operations to flush them out.
Another 38% of the region was deemed to have a permanent Taleban presence, meaning militants had established rural bases which were restricting local government activities and seriously compromising local administration.
Thousands attended a Taleban rally in Mingora just before the offensive
In those areas - three districts in FATA and 11 in NWFP - the Taleban had repeatedly shown their capability to strike at will, says the report.
Militants had made their presence felt by carrying out periodic attacks on girls' schools, music shops, police stations and government buildings.
The map gives a snapshot of the current situation. However continuing fighting between Pakistani troops and the Taleban means the situation on the ground could change in the future.
The Pakistani army's spokesman, Gen Athar Abbas, rejected the BBC map as "grossly exaggerated".
"The ground situation doesn't give any indicator of such influence or control of Taleban in this area," he told the BBC in Rawalpindi.
The region is notorious for its lack of law and order, so the researchers applied a series of rules to differentiate Taleban activity from general lawlessness.
The incidents had to be of a recurring nature, there had to be an official recognition of Taleban presence, Taleban militants must have appointed local "commanders" and religious schools sympathetic to the militants must be operating in the area.
Pakistan has been stepping up its campaign against the Taleban in the north-west.
Tens of thousands of people have fled from the region to escape the fighting.
The research also indicates areas to which researchers believe Taleban-style militancy may further spread inside Pakistan.
The report found that, based on current perceptions of religiously motivated violence, there were strong indications that in 47% of Punjab Province there was a high likelihood of an increase in Taleban militancy in the near future.
The BBC's Barbara Plett in Islamabad says that while the research indicates the strength of the Taleban in the region, the various factions and groups are only loosely co-ordinated.
Observers have warned against overstating the existence of one unified insurgency against the state, says our correspondent.
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