"Drones indeed are challenging our sovereignty. Of course, we have taken this matter up very seriously. I think this is a very serious issue, and our concern must be understood properly," Sharif said.
Sharif spoke to reporters from Raiwind, his family's estate outside Lahore, two days after the PML-N achieved a resounding victory in historic general elections.
"I think we have good relations with the United States of America. We certainly have to listen to each other," he said.
"If there are any concerns on any side, I think we should address those concerns," the 63-year-old leader said.
The CIA's drone attacks, targeting Al Qaeda and other militants in the tribal regions, have been controversial in Pakistan.
The Peshawar high court last week declared that drone strikes in Pakistan's lawless tribal belt were tantamount to a "war crime" and the armed forces had the right to shoot down the CIA-operated spy planes.
The court also directed the foreign ministry to move a resolution against the drone attacks in the United Nations.
US officials have said the drones target Al Qaeda and Taliban elements in Pakistan's tribal regions who are blamed for cross-border attacks in Afghanistan. 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. But a number of civilians have also died in the attacks.
Sharif also said he would facilitate the US withdrawal from Afghanistan scheduled for 2014 and extend full support to it.
"We will see that everything goes well and smoothly," he said.
Pakistan, which occupies a strategic location next to Afghanistan, will play a key role in any reconciliation deal with Taliban militants there.
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