"Secondly, a joint commitment to sustainable development and to improving health and education across Pakistan, especially in its border areas, where Britain will target much of our £650m development programme.
"Third, an understanding that conflict in Afghanistan has placed pressures on Pakistan and therefore a new commitment from Pakistan to work for stability and to promote reconciliation as we are doing in Afghanistan.
"And, of course, of paramount importance, a commitment to normalised relationships between India and Pakistan."
He said "today's stronger relationship" between the UK and Pakistan sent a signal that "we will work together to protect each other" and defeat terrorism.
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 nuclear arsenal was in safe hands.
He also dismissed a map produced by the BBC, which suggests only 38% of Pakistan's North West Frontier Province (NWFP) and surrounding areas are under full government control.
Mr Zardari told the BBC it was an "incorrect survey".
On Tuesday, Pakistan stepped up its campaign against the Taleban after dropping troops by helicopter to tackle a stronghold in the country's north-west.
The army has been fighting to retake large parts of its north-west frontier that has fallen to the Taleban.
Hundreds of thousands of people are reported to have fled the fighting and human rights campaigners are urging the army and Taliban to avoid civilian casualties.
Mr Zardari's visit comes after Britain announced a big aid increase for Pakistan to tackle the radicalisation of students into Taleban fighters.
Britain's aid budget for Pakistan over the next three years will be bigger than that for neighbouring Afghanistan.
The BBC's international development correspondent, David Loyn, said Mr Zardari, who became Pakistan's president after his wife Benazir Bhutto was killed during an election campaign, has shown willingness to work with Britain and America.
But the BBC correspondent said there were still big question marks over whether Pakistan's intelligence service had cut its long-standing ties with the Taleban, which Mr Zardari insists it has.
Mr Loyn said: "Britain's new strategy for the region, announced last month, involves a big increase in aid.
"Most of it will go into education to combat the influence of extremist Islamic schools - madrassas - many of whose students become Taleban fighters."
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