The opposition groups, led by cricketer-turned-politician Imran Khan and Canada-based cleric Tahirul Qadri, are protesting to press Sharif to call fresh polls alleging rigging during last year's elections.
"Under no circumstances, we will accept this (last) election. I am sitting here, Nawaz has one option. Resign and order a re-election," Khan, who heads the opposition Pakistan Tehreek-e-Insaaf party, said.
"I will not leave here until I have got real freedom for the country," Khan said, as he addressed his supporters amid rains.
The protesters reached here from Lahore after travelling more than 300 kms in over 35 hours.
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Khan announced that he will stage a sit-in from 3 pm today till Sharif resigns. Senior leaders of his party and workers also echoed similar sentiments and chanted "Go Nawaz Go" slogans.
The rain and journey took toll on Khan's health who had not slept for 40 hours, his supporters said.
According to Pervez Khattak, his party's chief minister in Khyber-Pakhtunkhwa province, Khan was suffering from high fever. He asked party workers to pray for Khan's quick recovery.
"The whole thing will be very peaceful. The government has to resign, and the assemblies have to be dissolved and the new system has to take their place," Qadri told media ahead of his arrival in the capital.
He could not address his supporters after reaching Islamabad due to his poor health and will meet them later in the day.
Qazi Faiz, spokesman of Qadri, said that the cleric was suffering from a sour throat but will address workers.
The political instability comes at a time when Pakistan is waging a war against militants -- particularly in the restive tribal regions along its border with Afghanistan.