Abbas' announcement came following talks with Egyptian President Hosni Mubarak, who had mediated the recently collapsed six-month truce.
Meanwhile, Foreign Minister Tzipi Livni is scheduled to visit Cairo Thursday for talks with Mubarak about a new truce.
Palestinian armed factions in Gaza had said Monday they were observing a 24-hour halt to rocket fire against Israel at the request of Egyptian mediators.
Despite the announcement, Gaza militants fired two Qassam rockets and one mortar round into the Negev over the course of the day.
The rockets fired Tuesday exploded in the Eshkol and Sha'ar Hanegev regions, causing neither casualties nor property damage.
Earlier Tuesday, Israel Radio quoted an Islamic Jihad official as saying the Palestinian militant group had only agreed to the respite to allow the entry of humanitarian goods into Gaza, and would shortly renew rocket fire against Israel.
Hamas spokesman Fawzi Barhoum, meanwhile, said Tuesday that Hamas and other Gaza factions were now prepared to study offers to renew the accord.
Another Hamas leader, Mahmoud Zahar, has said that his Palestinian militant group is willing to renew the recently ended truce in Gaza with Israel.
Zahar made the comments in an interview with the Egyptian newspaper Al-Ahram that was published on Tuesday. He told the paper that Hamas would agree to renew the cease-fire under its previous conditions.
He also said Hamas will evaluate the current situation in light of the six-month truce having ended last week. Zahar added that if there are positive responses within the organization to the proposal of returning to the framework of previous truce, Hamas will advance it.
On Monday, Zahar told Israel's Channel 10 TV that the truce could be restored.
"The price is the lives of the Palestinian people," he said.
Zahar demanded regular food and electricity supplies from Israel along with stopping Israeli military actions in the West Bank as well as Gaza.
Israel did not agree to halt operations in the West Bank under the truce that expired Friday, but Zahar's interview on an Israeli TV channel indicated that Hamas is interested in negotiating another cease-fire.