"Drone attacks are violating our sovereignty as well as international laws. Drone attacks must stop. We have protested many a time. This is simply unacceptable," Sharif was quoted as saying in a statement issued by his office yesterday.
Pakistan is "ready to facilitate the withdrawal of coalition troops from Afghanistan and hopes that the Afghan army and security forces would be able to manage the situation" after the drawdown of US and allied forces next year, Sharif said.
The protest was lodged on the instructions of the Prime Minister, the Foreign Office said.
Former envoy Tariq Fatemi, a Special Assistant to the Prime Minister, handed over a demarche to the US diplomat.
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The drone strikes have emerged as a key irritant in Pakistan-US ties.
American officials have defended the use of drones, saying they are vital for targeting Taliban and al-Qaeda elements sheltering in Pakistan's tribal belt.
On May 29, the deputy chief of the banned Tehrik-e-Taliban Pakistan, Waliur Rehman, was killed in another drone strike in North Waziristan.
Sharif spoke out publicly against the drone strikes for the first time shortly after he was formally elected Prime Minister by the lower house of parliament on Wednesday.
He said the attacks should stop as they were a violation of Pakistan's sovereignty.
Since 2004, the US has carried out over 350 drone strikes inside Pakistan, killing some of the top al-Qaeda and Taliban commanders. A number of civilians also died in the attacks.