It comes after Thursday's vote saw delayed results and violence - with 28 people killed in militant attacks.
Sharif's PML-N party won the most seats by a single party.
But supporters of imprisoned Khan, who ran as independents after his party was barred from the polls, won the most seats overall.
Sharif said his party would try to form a coalition government after failing to win a clear majority on its own.
Khan's PTI party released an audio-visual message created using AI and shared it on his X social media account.
In it, Khan rejected Sharif's claim to victory and urged his supporters to celebrate and protect their vote.
Independent members cannot form a government on their own, but they have the option to join any party after the elections.
