Hamas and other militant groups say they have accepted an Egyptian-brokered ceasefire to end two days of intense fighting with Israel that had pushed the sworn enemies to the brink of a new war. But Israelis are burning tyres to show their anger at the agreement.
Tuesday's ceasefire did not appear to address any of the underlying issues, including the blockade and Hamas' vast arsenal of rockets, and it was unclear whether United Nations and Egyptian efforts toward a broader deal might resume.
Israeli officials confirmed Cairo had been involved in Tuesday's arrangement.
Israel Ziv, a retired general who once commanded the Israeli military's Gaza division, said Israeli Prime Minister Benjamin Netanyahu was running out of options for dealing with Hamas.
A Palestinian man working in Israel was killed after a rocket hit the building he was in.
A Hamas official said the violence erupted on Sunday when a group of its members were fired upon by a passing auto belonging to Israel forces.
Among the dead were Hamas commanders Nour Baraka and Mohammad Al-Qarra, medical officials said.
"Hamas and the Palestinian Islamic Jihad made a deliberate decision to try to maximize damage inside Israel and to kill Israeli civilians", said Lt. Col. Jonathan Conricus, Israeli Defense Forces spokesman.
The southern Israeli city of Ashkelon is just eight miles from Gaza, making it an easy target.
Hamas, which has ruled the packed and impoverished coastal enclave since 2007, claimed victory and celebrations broke out.
Israeli Security Minister Yuval Steinitz said after a seven-hour cabinet debate that he knew of no formal truce.
While many Palestinians celebrated in the streets, in Israel the response was mixed.
Dozens of residents of bombarded southern villages blocked an Israeli traffic junction and burned tyres in protest at what they deemed a government capitulation.
In aerial attacks on Tuesday, Israel's military said it took out a rocket-launching squad and fired at several Palestinians infiltrating through the border fence around Gaza, which Israel keeps under blockade.
Since Monday, Israeli air strikes have killed seven Palestinians.
Israel had allowed Qatar to bring $15 million into Gaza for salaries as well as fuel to ease an electricity shortage, as part of understandings aimed at calming the border, where protests have triggered frequent clashes since March 30.
Palestinians in Gaza faced widespread destruction after the Israeli military targeted 160 sites.
Israel maintains a crippling blockade of the Palestinian enclave to isolate Hamas and prevent it from building up its military capabilities.