The tensions between Mr Zardari and Mr Sharif date back to the 1990s, but the two formed a brief partnership in government after parliamentary elections in February 2008.
Mr Sharif's PML-N left from the alliance in August 2008, complaining about the PPP's reluctance to reinstate former Chief Justice Iftikhar Chaudhry and other judges sacked by President Musharraf.
Relations have been further strained in recent weeks by a Supreme Court decision to ban Mr Sharif and his brother Shahbaz from elected office, and President Zardari's decision to put their stronghold in Punjab province under direct rule from Islamabad.
Shahbaz Sharif was Punjab's chief minister.
But on Saturday, in a move seen as a conciliatory gesture, the government agreed to seek a review of the Supreme Court ruling.
The political instability comes as Pakistan faces an economic crisis and a growing militant insurgency based in the north-west.
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