He said the most important job for the Palestinians was to form a government of non-partisan technocrats, repeating a demand by the Western powers who consider Hamas a "terrorist" group and refuse to negotiate with its representatives.
Suleiman said such a government would be able to "communicate with the world" in an effort to lift the Israeli-led blockade on Gaza, oversee reconstruction efforts and prepare for elections.
"I do not want to remind you of the consequences of, God forbid, failure," Suleiman said.
"We face a precious opportunity that may not be repeated".
Western nations opposed a previous unity government led by Hamas after the group won parliamentary elections in 2006.
Diplomats and analysts see the success of the Egyptian-sponsored talks as vital to reuniting Palestinians after 21 months of divisions between Hamas ruled Gaza and the West Bank, which is controlled by Fatah, the faction headed by Mahmoud Abbas, the Palestinian president.
On Saturday, Salam Fayyad, the Palestinian prime minister, said he planned to resign by the end of March to make way for the formation of the unity government.
Abbas, who appointed Fayyad after Hamas defeated Fatah in Gaza in 2007, asked him to remain in office until results emerged from the talks in Cairo.
Participants in February's talks said the five committees would have an agreement by the end of March.
However, a senior Hamas official said at the time it would take more than a few days to agree on the government.
Also attending Tuesday's talks were Ahmed Aboul Gheit, the Egyptian foreign minister, and Amr Moussa, the Arab League secretary-general.