Two opposition groups, led by Khan and Canada-based cleric Tahirul Qadri, plan to converge on Islamabad to press Sharif to call an early election little over a year after his landslide victory in the polls.
Shots were fired at Pakistan Tehreek-e-Insaf (PTI) chief's vehicle but he was not injured, Imran Khan's spokeswoman Aneela Khan said.
The convoy was also attacked in Gujranwala by a stone-throwing mob and police did not intervene, she said.
Confirming the incident of firing at Imran's convoy, Awami Muslim League leader Sheikh Rasheed said that they were attacked four times, and alleged that everything happened in the presence of police.
He also alleged that this happened on the orders of Sharif.
Imran Khan said that it was the PML-N activists who were standing above a police van and pelting stones at his supporters. Television pictures showed people tearing up posters featuring Khan's party and clashing with his supporters.
The anti-government protesters of both the groups plan a mass rally in Islamabad to press their claims, at the end of a ‘long march’ - which set off on a 370-km journey to the country's capital on Thursday.
Khan initiated his 'Azadi March' from Zaman Park, Lahore, while Qadri launched his 'Inqelab March' (revolution march) from the Model Town area of the city.
Khan's march had reached the industrial town of Gujranwala, about 70 kilometres north of Lahore.
Media reports said Qadri's convoy of the Pakistan Awami Tehreek (PAT) movement, was further along the road to Islamabad than PTI.
The PAT convoy has been divided into three parts, of which one has reached Jhelum, about 120 kilometres south of Islamabad, comprising about 8,000 to 10,000 people. The other two are expected to reach soon.
Further, all three convoys are going to gather in Jhelum, before proceeding to Islamabad.
Khan, speaking to reporters in Gujranwala, said "the time has come for Nawaz's monarchy to end, and to start a Naya Pakistan. One million PTI supporters will reach Islamabad."
"We have enough power right now to topple the government," he said.
"Gujranwala packed with PTI workers - I addressed them on the outskirts of the city. The Junoon is as strong as ever," Khan tweeted.
Addressing his supporters in Kharian, PAT chief Qadri said his party had received reports of a possible attack on their convoy after which they changed their strategy.

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