Crowds were also seen celebrating after claiming victory in several skirmishes, in which they seized stun grenades and ammunition abandoned by police, as they advanced towards D-Chowk Square, which houses key government buildings.
Inside the square, a traditional rallying point for protests, the demonstrators ransacked vehicles and set a police kiosk on fire.
More protesters, travelling on decorated trucks, were still heading for the capital on Tuesday as police appeared unable to stop them as they blocked the Karakoram Highway, the main road to Islamabad.
Khan, a former cricketer who served as Prime Minister from 2018 until he was ousted in 2022, has been in jail for more than a year.
The 72-year-old faces more than 150 criminal cases, which his party, the Pakistan Tehreek-e-Insaf (PTI), says are politically motivated.
Ali Amin Gandapur, the new PTI leader, has called for a sit-in at D-Chowk until their demands are met, but asked his followers on Tuesday to “protest peacefully”.
The PTI has demanded the Government, now led by Prime Minister Shehbaz Sharif, release “political prisoners” and “return the stolen mandate”, a reference to allegations that the election was rigged against the PTI.
“It is not a peaceful protest. It is extremism,” Sharif said on Tuesday, adding that the demonstrations were trying to achieve “evil political designs”.
According to the Interior Minister, Mohsin Naqvi, four security troops were killed when protesters rammed them with a vehicle on Srinagar Highway.
“We have now allowed police to take any decision according to the situation,” Naqvi said on Tuesday.
Earlier, he threatened that security forces would respond with live fire to the protesters.
Syed Zulfi Bukhari, a PTI spokesman, claimed on Tuesday that “paramilitary rangers shot live ammunition” at protesters in Islamabad, killing two civilians and injuring another 30.
Shahzor Ali, who is taking part in the protests, said people were on the streets because Khan had called for them to be there. “We will stay here until Khan is among us. He will decide what to do next.”
Shahid Khan, another passionate supporter of the former Prime Minister, told local media: “For Khan, I am ready to sacrifice every drop of my blood. Khan is our lifeline, and we won’t go back until he is released.”
Sania Ahmad, a young protester, added: “Khan is enduring extreme torture for us, and we will sacrifice our lives for him.”