"We respect the sovereignty of others and they should respect our sovereignty and independence. This campaign must come to an end," Sharif told MPs in his first address since being re-elected to the top post.
He told MPs that it was necessary to work out a joint strategy to stop the CIA-operated drone strikes in Pakistan's unruly tribal areas.
"We must learn others' [American] concerns about us, and express our concerns about them, and find a way to resolve this issue," he said.
However, Sharif gave few details on how he might bring about an end to drone strikes, which many in Pakistan see an affront to Pakistani sovereignty. Washington regards the drone attacks as a vital weapon against militants fighting US-led forces in Afghanistan.
Last week, Sharif had expressed his "serious concern and deep disappointment" at a drone strike carried out in North Waziristan on May 29 that killed Waliur Rehman, the second-in-command of the Tehrik-e-Taliban Pakistan.
"The drone attack was not only a violation of the country's sovereignty and territorial integrity, but also an action that has been declared as a violation of International Law and the UN Charter," Sharif was quoted as saying in a statement issued by the PLM-N.
The Peshawar High Court last month had declared that drone strikes in Pakistan's lawless tribal belt were tantamount to a "war crime" and the armed forces would have the right to shoot down the CIA-operated spy planes.
The court also directed the Pakistani Foreign Ministry to move a resolution against the drone attacks in the United Nations.
US President Barack Obama, in his most expansive discussion of the drone programme, said last month that he is haunted by the unintentional deaths. But he argued that targeted strikes result in fewer civilian deaths than indiscriminate bombing campaigns.
Pakistan insists that the US spy planes kill innocent people, damage civilian property and are counter-productive to the war on terror.
Since 2004, the US has carried out over 350 drone strikes inside Pakistan, killing some of the top al-Qaeda and Taliban commanders.
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