Canada-based cleric Tahirul Qadri asked his supporters to guard all entry and exit points of the building and not let anyone move in or out of it until Sharif resigns.
Qadri and opposition leader Imran Khan have been leading separate protests for the past seven days to force Sharif's resignation over alleged rigging in the 2013 elections.
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"It is time to besiege the parliament," Qadri said as he addressed his followers in front of the building.
"You will not allow anyone to enter or leave [the building], not even a mosquito... Not even the prime minister," the cleric said in his address.
Following the speech, hundreds of protesters wielding shields and sticks moved closer to the gates of the parliament and other buildings, ignoring warnings by police not to approach closer.
It is not known how many lawmakers are inside the building.
Sharif was also attending the session but there are reports that he safely left the building and reached his official residence.
Geo TV reported that some protesters also tried to march to the Prime Minister's house but police stopped them.
As the protests intensified, the military called for dialogue between the government and leaders of two major protests.
Army spokesman General Asim Bajwa made the call for dialogue on his Twitter account.
"[The] situation requires patience, wisdom and sagacity from all stakeholders to resolve prevailing impasse through meaningful dialogue in larger national and public interest," he said.
He said the buildings in the Red Zone are symbol of state and being protected by army, so the sanctity of these national symbols must be respected.
Sharif also decided to meet Khan in an effort to end the anti-government protests.
"It has been decided PM (Sharif) will meet Imran Khan for the sake of country," Minister for Railways Khawaja Saad Rafique, a close aide of Prime Minister Sharif, tweeted.
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