Among the targets hit by Israel in Gaza on Tuesday, he said, was a tunnel built to attack Israel.
Israel has fought three wars with Hamas since 2008.
The last war, in 2014, was especially devastating, with over 2,000 Palestinians killed, including hundreds of civilians, and widespread damage inflicted on Gaza's infrastructure in 50 days of fighting. He said the factions, including Islamic Jihad, would agree to the cease-fire as long as Israel did the same.
Israel stopped short of officially confirming any formal truce with Hamas and Islamic Jihad, which it regards along with the West as terrorist organizations.
Earlier, a senior member of Hamas said a ceasefire agreement had been reached with Israel.
In a statement the group's spokesman said after Egyptian mediation a "ceasefire agreement was reached with Israel to return to calm".
"It all depends on Hamas", Israeli Intelligence Minister Israel Katz said on Israel Radio.
TRT World spoke with Tel Aviv-based journalist Jan Franke for more.
The United States called for an emergency meeting of the United Nations Security Council to discuss the attack on Israel. Explosions shook the impoverished territory, which has been blockaded by Israel for more than a decade, and smoke rose from areas hit. While Israeli officials have not confirmed the rumors, the IDF has not launched any new strikes.
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Daoud Shehab, an Islamic Jihad spokesman, said Egyptian officials had been in contact with the group to try to restore calm.
Prime Minister Benjamin Netanyahu pledged a forceful response to the barrage of mortar shells fired.
Itamar Yaar, former deputy head of Israel's National Security Council, said it was unlikely that the latest escalation would lead to another war, mainly because neither side is interested in such a confrontation. "I don't think serious people in Israel want to reoccupy Gaza", said Yaar.
The Israeli military said most of the projectiles were intercepted, but three soldiers were wounded, raising the chances of further Israeli retaliation.
This follows weeks of Palestinian mass demonstrations near the fence with border.
Lieutenant-Colonel Jonathan Conricus, a spokesman for the Israel Defense Forces (IDF), said the most extensive strikes from Gaza since the 2014 war also drew "the largest IDF retaliatory attack" since that conflict.
Among those associated with RSY-Netzer to attend was Nina Morris-Evans, who said: "By Jewishly mourning the lives lost, we were not condoning terrorism, Hamas or violence of any form".
The Israeli action had prompted Palestine to askthe International Criminal Court (ICC) to open an "immediate investigation" into Israeli "crimes" committed against the Palestinian people.
Highlighting Washington's isolation on the Israeli-Palestinian issue, Kuwait - a non-permanent Security Council member that represents Arab countries - hopes to win a high number of votes in favour of its proposal.