Despite heavy rain, crowds of protesters tried to break through police lines to push their way to the prime minister's residence. Police responded by firing teargas.
Protesters led by Imran Khan, a renowned cricketer before entering politics, and fiery cleric Tahir ul-Qadri, erupted last month and descended into deadly confrontation on Saturday, with at least three people killed in clashes with police.
In a nation where power has often changed hands through military coups rather than elections, the army is bound to play a key role in how the conflict unfolds but it has not directly intervened, apart from talking to the protagonists and calling on them to show restraint.
Sharif, who swept to office last year in Pakistan's first democratic transition of power, has refused to resign. He is due to address both houses of parliament on Tuesday in an apparent effort to show that he is firmly in control.
Khan, who has refused to hold negotiations and says he would not call off protests until Sharif resigns, has called on his supporters to keep fighting.
In a warning to police, the military said any further use of force to resolve an escalating political crisis would only worsen the situation. But it has also said the crisis had to be solved through talks, in a clear message to the protest leaders.
As protesters charged towards police lines in the so-called Red zone - home to the prime minister's house, parliament and many foreign embassies - security forces could be seen retreating, with police huddled in groups and avoiding direct confrontation.
Reflecting concern about security in the capital, all schools were closed on Monday, the start of a new academic year.