Mr Zardari says the survival of PPP is linked to the survival of PML-N
The leader of the Pakistan People's Party (PPP), Asif Zardari, has appealed to former prime minister Nawaz Sharif to rejoin the governing coalition.
Mr Sharif pulled his PML-N party out of the coalition on Monday after a dispute over the reinstatement of judges sacked by former president Pervez Musharraf.
The two sides also disagree over who should be the next president.
Mr Sharif's party has put forward its own candidate to run against Mr Zardari in the 6 September presidential poll.
The split in the coalition has created fresh political uncertainty in Pakistan, as it faces a deteriorating security situation and a declining economy.
In a televised address, Mr Zardari said: "We are sad over Nawaz Sharif's decision. We want to move together and solve the problems facing the nation.
"We will request Nawaz Sharif to return to the government," he said.
Mr Zardari said the survival of the PPP and PML-N were interlinked. He said the PPP wanted Mr Sharif's support in its effort to strengthen democratic institutions.
Mr Sharif said he was abandoning the coalition because the PPP - led by Asif Zardari, the husband of the assassinated Benzir Bhutto - had broken too many promises.
He accused the PPP, among other things, of failing to honour agreements to re-instate judges sacked by the Mr Musharaaf, who resigned last week.
Mr Zardari said he would "seek forgiveness" from Mr Sharif if "his feelings are hurt".
"I want to take Nawaz on board as there are immense difficulties ahead. Perhaps I cannot tell the whole truth to the nation," he said.
Analysts say the PPP fears that if the judges are reinstated, they may revoke an amnesty that paved the way for Mr Zardari and Ms Bhutto to return to Pakistan last year - leaving Mr Zardari open to prosecution on long-standing corruption charges.
The two parties are also at odds over who should become Pakistan's next president.
Mr Zardari filed his nomination papers for the presidency at the election commission office on Tuesday.
Meanwhile, Mr Sharif announced his party's candidate as the former Supreme Court chief justice, Saeeduzzaman Siddiqui.
Last week militants killed nearly 70 people in one attack alone
The two party leaders had agreed to reduce the powers of the presidency in a country where the president has in the past dismissed democratically elected governments.
Mr Sharif says as long as the presidency remains a powerful post, a non-partisan candidate acceptable to everyone, rather than Mr Zardari, should have been agreed on.
The BBC's Charles Haviland in Islamabad says the PPP has other parties in the coalition and the government will not fall.
But our correspondent says the PPP may find Mr Sharif to be an uncomfortably powerful figure to have in opposition at a time when the country lacks a sense of political direction.
Mr Zardari and Mr Sharif worked together to threaten Mr Musharraf with impeachment, which led him to resign last week.
The US gave huge financial backing to Mr Musharraf during his nine years as president as Pakistan became a key ally in Washington's so-called "war on terror".
Washington is concerned that an insurgency is gaining strength in Pakistan and that the coalition's current policy of negotiating with militants is not working.
Last week a double suicide attack at a munitions plant in the town of Wah in Punjab province left nearly 70 people dead.
The Pakistan Taleban claimed responsibility for what was the heaviest attack on a military installation by a militant group in the country's history.