Zardari made the remarks during a meeting with the US Special Representative for Afghanistan and Pakistan, Marc Grossman, at Dushanbe in Tajikistan on Sunday. Both leaders are in Tajikistan to attend a regional conference on Afghanistan beginning on Monday.
Zardari said the US drone attacks violated Pakistan's sovereignty, were counterproductive and fuelled militancy because of civilian casualties. "He called for an end to drone strikes," presidential spokesman Farhatullah Babar said in a statement.
The Pakistan president also indicated to Grossman that Pakistan intended to go ahead with a gas pipeline project with Iran despite international pressure. He drew Grossman's attention to the energy crisis in Pakistan and said the pipeline project, concluded years ago, should be seen as vital to solving the country's energy problem and its economic development. He drew Grossman's attention to the "need for greater transparency in the relationship" and said Pakistan wants to "re-engage with the US at all levels in the light of the parliamentary review which would be completed soon," Babar said.
A joint session of Pakistan's parliament will resume on Monday debating recommendations for new terms of engagement with the US.
The government ordered the parliamentary review after 24 Pakistani soldiers were killed in a cross-border North Atlantic Treaty Organisation air strike in November.
Zardari said the parliamentary review, which "was long overdue", as a manifestation of democracy taking roots in Pakistan and of elected representatives "taking ownership of one of Pakistan's most important bilateral relationships".
The effort had to be "to work within the parameters set by the parliament and not to bypass it," he said. He said Pakistan wanted to revive the relationship with the US on the basis of mutual respect and mutual interest.
During the talks with Grossman, Zardari called for increased access to US markets for Pakistani exports through preferential tariffs. He also raised the issue of drug trade, which he said is providing "financial sustainability to militants" and sought international efforts to curb the menace.
Large quantities of opiates enter Pakistan from across the border and the US and North Atlantic Treaty Organisation forces should interdict the movement of drugs to end the financial sources of militants, he said.
The president further told Grossman that Pakistan believed peace and stability in Pakistan depended on peace and stability in Afghanistan and that Islamabad would continue fighting militants till the logical end.
Grossman said the US respected Pakistan's territorial integrity and sovereignty and "expressed respect for Pakistan's ongoing parliamentary review" of relations with the US, said a statement from the US embassy in Islamabad.
The US and Pakistan "have many shared interests and common goals that we can act on together", Grossman said. The US wants an "honest, constructive, and mutually beneficial relationship with Pakistan and remains committed to continued engagement", Grossman said.
The US Special envoy and Zardari discussed regional stability and security, including efforts to support an Afghan peace process. Grossman described Pakistan's recent call for insurgents to join an Afghan peace process as "welcome and helpful".
"They also discussed the importance of counter-terrorism cooperation against insurgents who would harm Afghans, Pakistanis, and Americans," the US embassy statement said.
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