The official, at a joint command centre in Gaza, said the groups, in cross-border violence over the past two days, had been "responding to crimes" by Israel—a reference to the killing on Tuesday of two gunmen from the Hamas militant organisation.
"Factions of the resistance consider this round of escalation over as far as we are concerned, and the continuation of calm depends on the behaviour of the occupation," the official said, using militant factions' term for Israel.
The Israeli military declined to comment on the official's remarks.
Earlier, a pregnant Palestinian woman with her 18-month-old child, and a Hamas terrorist, were killed in the Israeli attacks, and at least five civilians were wounded, local medical officials said.
The Israeli military said at least 23 people were wounded in southern Israel. One was identified by her employer as a Thai agricultural worker.
The flare-up came after officials on both sides had talked about potential progress in an effort by the United Nations and Egypt to broker a truce to end months of violence and alleviate deepening humanitarian and economic hardship in the Gaza Strip.
The latest fighting has stayed within familiar parameters. The rocket fire from Gaza has not targeted Israel's heartland and the Israeli military said its air strikes were limited to Hamas installations.
Yuval Steinitz, a member of Prime Minister Benjamin Netanyahu's inner cabinet, told Israel Radio before the Palestinian officials comments that Israel was "not eager for war" but would make no concessions to Hamas.
Netanyahu was due to hold a security cabinet meeting later in the day after consultations with security officials.
Rocket warning sirens sounded almost non-stop in the southern Israeli town of Sderot and other border communities from sunset on Wednesday. Many residents took shelter in safe rooms in their homes. The military said more than 180 rockets and mortar bombs were fired from Gaza.
Ambulance sirens echoed through the night in Gaza, where families huddled at home as powerful explosions shook buildings. The Israeli military said its aircraft struck more than 150 facilities belonging to Hamas.
UN Middle East envoy Nickolay Mladenov said in an overnight statement: "I am deeply alarmed by the recent escalation of violence between Gaza and Israel, and particularly by today's multiple rockets fired towards communities in southern Israel."
The United Nations, he said, has engaged with Egypt in an "unprecedented effort" to avoid serious conflict, but cautioned that "the situation can rapidly deteriorate with devastating consequences for all people".