* Fighting continues into second day
* Egypt seeking ceasefire
* Minister says Israel not eager for new Gaza war
A long-range rocket fired from Gaza struck an uninhabited area outside the largest city in southern Israel on Thursday, Israeli Army Radio reported, hours after a Palestinian official said an end to a surge in cross-border fighting could be near.
Army Radio said the rocket was a long-range Grad capable of reaching Israel's heartland and that it hit an open area outside Beersheba.
It was a show of force and defiance by Palestinian militants ahead of a meeting of Israeli Prime Minister Benjamin Netanyahu's security cabinet, where terms for a possible truce were likely to be on the agenda.
Rocket alert sirens sounded in Beersheba, a city of 200,000 inhabitants some 40 km from the Gaza Strip, for the first time since the 2014 war between Israel and militants in the Palestinian enclave.
Hours earlier, a Palestinian official said armed factions in Gaza were prepared to halt a round of rocket attacks on southern Israel - where communities near the border had been targeted - if the Israeli military stopped its air strikes after two days of violence.
A pregnant Palestinian woman and her 18-month-old child, and a militant from the Hamas group that rules Gaza, were killed in the Israeli attacks, and at least five civilians were wounded, local medical officials said.
The Israeli military said seven 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.
"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 Palestinian official said, using militant groups' term for Israel.
The Israeli military declined to comment on the official's remarks.
The official, at a command centre used by armed groups in Gaza, said they had been "responding to crimes" by Israel - a reference to the killing on Tuesday, in disputed circumstances, of two Hamas gunmen.
Yuval Steinitz, a member of Netanyahu's inner cabinet, told Israel Radio before the Palestinian official's comments that Israel was "not eager for war" but would make no concessions to Hamas.
Before the Beersheba incident, Israeli officials said Netanyahu was due to hold the security cabinet session 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 have a reinforced room in their homes where they can shelter. 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 the United Nations had 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".