But their dispute resurfaced when the PPP insisted the reinstatement of the judges, including Iftikhar Muhammad Chaudhry, the former chief justice, be done via a constitutional package that would include plans for judicial reforms.
Sharif's Pakistan Muslim League-Nawaz (PML-N) insists on adhering to the system agreed upon in March and the 30-day time limit for the judges to resume their jobs.
Sharif told reporters before leaving for Dubai that he wanted the "coalition to stay together" but warned of "disastrous consequences for democracy and Pakistan" if the judges were not restored.
Kamal Hyder, Al Jazeera's correspondent in the Pakistani capital Islamabad, said there were "serious differences" after the coalition held a landmark meeting over a month ago in which they agreed to reinstate the judges through an act of parliament.
"Nawaz [Sharif] has rushed to Dubai to try to avert a major crisis, the first test of the coalition government," he said.
"A lot of analysts are saying that he may be willing to give Zardari more time to resolve the crisis as amicably as possible, but that is going to be a tall order.
"There are reservations, and people are waiting to see whether the coalition will carry on or break apart."
Party sources said the two sides had agreed on the text of the resolution, but the PPP was still pressing for constitutional changes.
"In addition to the agreement on the resolution, we have to work out modalities for implementing that resolution in line with the constitutional requirements," Farhatullah Babar, a spokesman fo the PPP, told AFP.
The PPP said Zardari and Sharif were expected to meet around midday in the Gulf emirate, where Zardari - the widower of Benazir Bhutto, a former premier killed in December - is staying with his two children.
The Pakistani legal community and a number of political parties that boycotted the general elections on February 18 are threatening to launch a protest movement if the judges are not restored.
Stand on judges
The PPP won a majority of seats in the 342-member national assembly, or lower house of parliament, but not enough to form a government on its own. The polls, however, dealt a crippling blow to Musharraf's supporters.
Sharif, whose PML-N secured the second largest number of seats in the polls, said his party had won a mandate from the people for its stand for the restoration of judges.
Sharif's trip to Dubai came after the apparent failure of talks between his younger brother Shahbaz, who is the PML-N's president, and Zardari in Dubai on Monday and Tuesday.