Israel and Hamas hadn't been able to come to an agreement over the weekend on a potential 24-hour cease-fire as a rocket from Gaza killed one Israeli soldier in the 19th day of fighting.
A 12-hour truce between the two sides expired at 8 p.m. local time Saturday, or 1 p.m. ET. Israel agreed to a four-hour extension of the cease-fire, but at the conclusion of the 12-hour period, rockets were fired from Gaza into Israel.
A second truce, for 24 hours, was proposed by the United Nations and Israel agreed as long as it could continue destroying tunnels leading from Gaza into Israel.
Hamas rejected the proposal and resumed rocket fire, killing one Israel Defense Forces soldier and injuring a civilian.
"Any humanitarian cease-fire that doesn't secure the withdrawal of occupation soldiers from inside Gaza's borders, allow citizens back into homes, and secure the evacuation of the injured is unacceptable," Sami Abu Zuhri, a Hamas spokesman, said in a statement late Saturday.
By Sunday, though, Hamas said it would agree to the 24-hour truce after the IDF resumed its attack.
"In response to the intervention by the United Nations and taking into account the conditions of our people and the upcoming Eid holiday, an accordance has been reached between Palestinian resistance groups to call a humanitarian calm for 24 hours," Zuhri said Sunday.
Israeli Prime Minister Benjamin Netanyahu said he is interested in a peace plan by Egypt.
"We hope we can get a sustainable quiet as soon as possible. I think the only path to do that is by adopting the Egyptian initiative," he said, referring to the demilitarizing of Gaza, and social and economic relief for its residents.
Hamas has rejected Egypt's proposal.
As of Saturday, 1,139 Palestinians and 45 Israelis have died in fighting that began July 19.
Notable deaths of 2014 [PHOTOS]