Nawaz Sharif's call came in his first speech in parliament, minutes after lawmakers elected him the country's premier.
But he gave little details on how he might bring about an end to the strikes, which many in Pakistan have called an affront to the country's sovereignty.
The U.S. considers the strikes vital to battling militants such as al-Qaida, who use the tribal areas of Pakistan as a safe haven.
Sharif's comments are in line with previous statements he has made calling for an end to the controversial strikes.
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