Speaking to thousands of supporters in Islamabad at the end of a nearly 40-hour anti-government march, Khan announced he would not end his sit-in until Sharif resigns, Xinhua reported.
"I am not going to leave this place, until true freedom is achieved for the nation," Khan said at Islamabad's Aabpara marketplace.
Khan led thousands of marchers into the Pakistani capital late Friday to stage sit-in and present demands.
The march was started Thursday from the eastern city of Lahore and the marchers arrived in Islamabad in nearly 36 hours.
The government has deployed around 30,000 security personnel including army troops to ensure security for the capital city.
Khan claimed that the 2013 elections had been rigged and that Sharif has a "fake mandate".
The government and the election panel have rejected his claim.
"I am going to stay here. Nawaz has only one option, he must resign and get re-elections done," Khan said.
"I will not accept rigged elections," Khan told the people participating in the Azadi (independence) March amid heavy rain in Islamabad.
He asked the marchers to gather again at the same place at 3 p.m. Saturday to begin a sit-in.
"The rigged election has to be challenged to safeguard democracy and the credibility of voting," Khan said.
He said his party leaders approached the Election Tribunals and Supreme Court with complaints about the massive rigging, "but no relief was accorded".
He said his long march poses no threat to the democratic system, adding that there is in fact "no democracy in our nation".
Khan's PTI rules the northwestern Khyber Pakhtunkhwa province and has also reasonable representation in the National Assembly.
A religious anti-government leader, Tahir-ul-Qadri, who heads the Pakistan Awami Tehrik (PAT) or Peoples Movement, has also arrived in Islamabad to start a sit-in.
Qadri will also speak to his marchers later Saturday.
Qadri said he intends to bring out a "revolution" as the present system has failed to deliver justice to the people.
The government had allocated two different locations for both parties to hold demonstrations.
The marches had been relatively peaceful during the 370 km journey. However supporters of the ruling Pakistan Muslim League-Nawaz clashed with the marchers in Gujranwala, a main city nearly 60 km from Lahore.
Several of Khan's supporters were injured after being hit by stones.
Some workers of the ruling party were arrested.
The government did not create any hurdles on the way of the marchers. However containers have been placed on roads leading to the Red Zone of Islamabad to stop the marchers from going there.
Sharif has ruled out threat to his government and ministers said no question arises of his resignation.
The government accuses Khan and Qadri of derailing the elected government and to stop the prime minister from his serious efforts to address the country's problems.