Hamas say they have agreed to a ceasefire with Israel to end the largest flare-up of violence between the sides since the 2014 war.
Khalil al-Haya, a senior Hamas official, said that Egyptian mediators intervened "after the resistance succeeded in warding off the aggression".
However Israeli Cabinet minister Naftali Bennett told Israel's Army Radio no agreement has been reached yet.
The Israeli military struck dozens of militant sites in Gaza overnight as rocket fire continued toward southern Israeli communities into early Wednesday morning.
Israeli sirens warning of imminent rocket and mortar strikes sounded late into the night and Israeli aircraft hit 55 militant targets in the Gaza Strip, including a cross-border tunnel under construction, the military said.
The armed wings of Hamas and Islamic Jihad claimed responsibility for the firing and said it was in response to Israel's killing of dozens of Palestinians since March 30, mainly in Gaza border protests.
Israeli Prime Minister Benjamin Netanyahu convened security chiefs, and Intelligence Minister Israel Katz said the country was "at the closest point to the threshold of war" since the seven-week conflict with Palestinian militants four years ago.
"If the firing (from Gaza) does not stop, we will have to escalate our responses and it could lead to a deterioration of the situation," Katz said on Army Radio.
Palestinian President Mahmoud Abbas, who heads the Fatah faction that is dominant in the occupied West Bank and is a bitter rival of Hamas and Islamic Jihad, said Israel had used "vigorous aggression" against Gaza that proved it did not want peace.
Al-Haya said militant groups in Gaza will commit to the ceasefire as long as Israel does.
The border area has been tense in recent weeks as Palestinians have held mass protests aimed at lifting an Israeli-Egyptian blockade imposed after Hamas seized power in 2007.