The Parliament is set to vote on a resolution aimed at bolstering the civilian leadership amidst a row with the powerful military.
Shortly after the Supreme Court issued a notice for contempt of court against Gilani for failing to reopen graft cases against Zardari, the premier called on the president and discussed the "current situation", a spokesman said.
Gilani then chaired a meeting of the parliamentary committee of the partners of the ruling Pakistan People's Party.
Zardari too joined the meeting held at the Prime Minister's House.
Top leaders of the parties in the ruling coalition took stock of the apex court's order and discussed their strategy for the parliamentary session to be held this evening.
The session of the National Assembly or lower house of parliament will vote on a resolution moved by the Awami National Party, a junior coalition partner, that seeks endorsement and support for "efforts made by the political leadership for strengthening democracy" and calls for reposing "full confidence and trust" in the leadership.
The resolution was moved in parliament on Friday against the backdrop of a confrontation between the civilian government and the powerful military over an alleged memo that had sought US help to prevent a feared military takeover in Pakistan after the killing of Osama bin Laden last year.
The Supreme Court accepted the military's request to order a probe into the memo scandal and appointed a judicial commission to conduct an investigation within four weeks.