Hamas' Al-Aqsa TV channel reported late on Thursday that a ceasefire has taken hold "on the basis of mutual calm". It added that the truce was mediated by Egypt and other unidentified regional players.
Israeli newspaper Haaretz quoted an unnamed senior Israeli commander as saying that the military is "nearing launching an operation in the Gaza Strip" if the current situation persists.
The announcement comes after a new round of strikes carried out by the Israeli Defense Forces, which said it targeted 150 military targets in response to 180 rocket launches from Gaza at Israeli territory.
The Israeli military said it only struck military targets, including production sites for weapons and tunnels.
On the Israeli side, at least seven people were wounded.
Gaza's Health Ministry identified those killed in the airstrikes from Wednesday to Thursday as Hamas fighter Ali Ghandour, 23-year-old Enas Khamash and her daughter Bayan. Khamash's husband, Muhammad, was severely injured during the strike.
Hamas is rumored to be demanding the release of a large number of Palestinian prisoners in exchange for the dead soldiers' return, a demand Jerusalem is said to reject.
A second Palestinian official with knowledge of the talks said the cease-fire would begin at 2045 GMT.
After four hours of discussion about the escalation in the south and the hard situation in which Israelis there are living, Israel's Ministerial Committee on National Security instructed the IDF to "continue to act with force against terrorist elements".
Israel and Hamas, the resistance movement that governs Gaza, agreed on a truce on Thursday to end a flare-up in cross-border fighting, two Palestinian officials said.
"For months I have been warning that the humanitarian, security and political crisis in Gaza risks a devastating conflict that nobody wants".
In Gaza's Nusseirat refugee camp, Sabreen Abu Shawiesh said installing solar panels on the metal roof of her one-floor house had changed her family's life: "We nearly had no electricity, nowadays fans are working all day".
"Our collective efforts have prevented the situation from exploding until now".
A source familiar with the negotiations said Egypt and the United Nations had negotiated a return to calm starting shortly before midnight Thursday, seemingly bringing an end to the upturn in violence.
Strikingly, the word "respond", or any variation thereof, appears only in context of Hamas responding to Israeli strikes: "Hamas, the Islamic militant group that has ruled Gaza for 11 years, has been trying to change the balance of deterrence in the area, responding to every Israeli strike against Gaza".
But the ceasefire will face its first test later in the day, as Palestinians in Gaza planned on resuming weekly border protests, which at times have become violent.
Hamas has led weekly border protests aimed in part at drawing attention to the Israeli-Egyptian blockade imposed after Hamas took control of Gaza. Most were killed by Israeli fire during the protests but others died in air strikes.
Most of the rockets fired by Palestinian militants landed in open areas, but at least two hit the Israeli town of Sderot near the Gaza Strip and sirens sounded throughout the night and into the morning.