Officials said Abbas would present Haniya with his formal letter of appointment on Tuesday evening, setting in motion the process of naming a cabinet to be approved by the Hamas-dominated parliament.
Haniya will have five weeks to form a government. The process of picking him as prime minister-designate is a mere formality after the election, when Hamas won 74 seats in the 132-member legislature.
Abbas' Fatah Party, which had dominated Palestinian life for four decades, won only 45 seats.
It was expected that Haniya would receive the official appointment on Monday.
Palestinian officials did not explain the delay, but Abbas has been pressing Hamas to moderate its anti-Israel positions and accept the idea of peace talks. Hamas has refused.
Nabil Abu Rdeneh, an Abbas aide, said further talks were set for Tuesday, when Abbas will give Haniya his official appointment.
Talking to reporters after the Monday meeting, Haniya said he would try to form a joint government "that can shoulder its responsibilities in the political area and internal issues."
Palestinian groups met to discuss
forming a coalition government
So far Fatah has refused to join.
Hamas is trying to convince other Palestinian factions to join a coalition, hoping to persuade the world that its broad-based cabinet represents all the Palestinians and should not be the target of a boycott.
Even before he takes office, Haniya has been shunned by Israel, the US and the Europe Union.
Israel froze the transfer of funds to the Palestinian Authority, and Western nations threatened to halt hundreds of millions of dollars of foreign aid when Haniya takes office.
The decision to freeze transfer of tax money collected for the Palestinians drew criticism from Haniya.
"This collective punishment will not break the determination of the Palestinian people"
"The Israelis are trying to starve innocent people by taking money from our taxes, and we are going to fight this by all legal means," he said.
"This collective punishment will not break the determination of the Palestinian people."
Raanan Gissin, an Israeli official, rebuffed charges that Israel was breaking the interim peace accord that mandates handing over the funds.
He said Israel is not obliged to transfer funds that could be used for terrorism, and Israel is not obliged to follow the agreement because "Hamas does not respect it."
Yuval Diskin, head of the Shin Bet security agency, said a Hamas entity next to Israel is a "strategic threat".
He told a parliamentary committee that Hamas could invite hardline groups like al-Qaida and Hizb Allah to operate in Palestinian areas.
"A Hamas state on the borders of Israel is a real threat. This will be a radical Sunni state that radical forces can reach from around the world."