Eight people have been killed in the worst escalation of violence Gaza has seen since the 2014 war.
A fresh wave of fighting erupted in the Gaza Strip, leaving an Israeli soldier and seven Palestinians dead after two days of unrest.
An Israeli aircraft fired towards a militant who was part of a group launching rockets at its territory, the Israeli military said.
The Israeli military said an Israeli soldier was also killed and another wounded after a firefight erupted.
It came as a man in southern Israel was killed after Gaza militants fired dozens of rockets at a residential building early on Tuesday.
Hamas and other militant groups have since said they had accepted an Egyptian-brokered ceasefire to end two days of fighting with Israel that had pushed the sworn enemies to the brink of a new war.
The escalation had risked derailing efforts by the United Nations, Egypt and Qatar to broker a long-term truce.
On Tuesday, the US condemned rocket and missile attacks from Gaza into Israel and said it stood with Israel.
“We condemn in the strongest terms the rocket, missile and mortar attacks that are taking place from Gaza into Israel,” US State Department spokeswoman Heather Nauert said at a news briefing.
“We call for the sustained halt of those attacks. We stand with Israel as Israel defends itself against these attacks. It is simply unacceptable to target civilians.”
The fresh cross-border attacks were triggered by a botched Israeli undercover raid into the Gaza Strip late on Sunday, marking the most serious escalation since an Israel-Hamas war in 2014.
One Hamas commander and six other gunmen were killed, while an Israeli commander also died in the raid.
About 400 rockets and mortars have been launched from Gaza since the current round began on Monday, with 100 intercepted by Israel’s Iron Dome defence system, the Israeli military said.
In Israel, at least 20 people have been wounded, several seriously.
Following the Palestinian deaths the armed wing of Hamas threatened to step up its attacks and fire rockets further north towards the Israeli cities of Ashdod and Beersheeba if Israel did not cease fire.
Over the past few months the two sides have come close to a major escalation several times, but have stepped back in favour of giving a long-term Egyptian mediated truce a chance.
In Gaza, schools, government offices and banks were closed on Tuesday while classes were cancelled in Israeli towns near the border.
Israeli Prime Minister Benjamin Netanyahu convened his cabinet to discuss their next move while the military said it had sent infantry and armoured reinforcements to the Gaza frontier.
He declared that he wanted to avert “unnecessary” war in Gaza.
Hamas, which is considered a terrorist group in the West, and Israel have fought three wars in the past decade.
(c) Sky News 2018: Eight dead in worst escalation of violence in Gaza since 2014