Sharif briefed the President about the measures taken by the government to peacefully deal with the protests by Khan and Qadri.
The Prime Minister also apprised the President on the law and order situation, specifically related to the storming of the sensitive 'Red Zone' by the protesters.
The Red Zone houses important government buildings including the Parliament House, Prime Minister House, President House, the Supreme Court besides the embassies.
Hussain told Sharif that being an elected prime minister, he should not resign but try and accommodate maximum demands of the protesters in order to defuse the tension, sources said.
The President asked the government to ensure the security of all key offices and the diplomatic enclave where foreign missions are located.
The office of the President is ceremonial in Pakistan but it becomes important in a political crisis due to his powers related to summoning of parliament and granting remission of punishment by the courts.
Hussain belongs to Sharif's party and was handpicked by him for the top job.
Meanwhile, Sharif also telephoned former president and Pakistan People's Party Co-Chairman Asif Ali Zardari and discussed prevailing political situation, Geo News reported.
Both the leaders exchanged views on Pakistan Tehreek-i-Insaf's 'Azadi March' and the Qadri-led Pakistan Awami Tehreek's 'Inquilabad March', the report said quoting sources.
Sharif and Zardari agreed that they would not compromise on sanctity of the constitution, it said.
The Pakistan government negotiators were to meet anti-government protest leaders to strike a deal to end the week-long political crisis and the siege of the Parliament by protesters who are demanding the resignation of the prime minister.
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