Police eventually pushed them back, and Islamabad police chief Tahir Alam warned that anyone attacking the police vans would be arrested.
Khan and Qadri arrived in the capital last month in massive convoys that had set out from the eastern city of Lahore. Since then thousands of demonstrators have been camped outside parliament demanding that Prime Minister Nawaz Sharif resign over alleged voting fraud in last year's election.
The protesters remained peaceful until August 30, when they tried to storm the prime minister's residence, prompting police to fire tear gas and rubber bullets. Three people were killed in the melee and hundreds more were wounded.
On Sept. 1, the demonstrators stormed Pakistan Television, briefly forcing the channel off the air.
On Saturday, Pakistan's Interior Minister Chaudhry Nisar Khan said police arrested only those involved in the attack on Pakistan Television and other government buildings. He urged Khan and Qadri to continue negotiating an end to the standoff.
Khan and Qadri have said they will not end their protests until Sharif resigns. Pakistan's parliament unanimously rejected their "unconstitutional demand" after Khan's party, the third largest political bloc, quit the assembly.
Sharif was forced from office after a previous stint as prime minister in 1999, when the then-army chief Pervez Musharraf seized power in a coup.
Elsewhere in Pakistan, a powerful car bomb exploded in a bazaar in the southwest, killing at least three people and wounding 24 others, police said.
Senior police officer Abdur Razzak Cheema said the attack took place when a vehicle carrying security forces was passing through the market in Quetta, the capital of southwestern Baluchistan province.
The dead included a paramilitary soldier and two civilians, he said.
Baluchistan is Pakistan's largest province and has been the scene of a low-scale insurgency for several years.
Separatists in the region are pressing the federal government to more equitably share the revenues from gas and oil extracted from the province.
Also Saturday, the head of a branch of the Pakistani Taliban said his group would give up armed struggle in favor of a preaching campaign to push for the imposition of Islamic law in the country.
Ismatullah Muawia, who heads the local Punjab chapter of the Pakistani Taliban, said in a video message that the group came to its decision after consulting with religious scholars. In Afghanistan however, it would continue to fight foreign forces operating there.
The move was the latest blow to the Pakistani Taliban, which last month saw several factions leave the organization to form a splinter group.
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Associated Press Writers Abdul Sattar in Quetta and Munir Ahmed in Islamabad contributed to this report.