The situation in Gaza "is on a knife-edge", UN Secretary General Ban Ki-moon has said, urging Israel and Palestinian militants to end hostilities.
Ban warned that the region "cannot afford another full-blown war".
His comments come after Israel said Hamas had fired dozens of rockets at Israeli cities on Wednesday night, following Israeli air strikes in Gaza.
More than 60 Palestinians are reported to have died since Tuesday in Israel air strikes against militants.
Gaza medical officials say half of the casualties were civilians, including women and children.
Seven Palestinians were killed in an air raid on two houses near the southern city of Khan Younis early on Thursday.
"The deteriorating situation is leading to a downward spiral which could quickly get out of control," Ban said.
"The risk of violence expanding further still is real."
He demanded that Hamas militants stop firing rockets and also urged the Israeli government to exercise restraint and respect international obligations to protect civilians.
The UN Security Council is due to meet for emergency talks on the crisis later on Thursday.
Israeli PM Benjamin Netanyahu earlier vowed to "further intensify attacks on Hamas" in Gaza, saying the militants would "pay a heavy price" for their rocket attacks.
Israel says its targets have been militant fighters and facilities including rocket launchers, weapons stores, tunnels and command centres.
GROUND OFFENSIVE POSSIBLE
Meanwhile, Israeli President Shimon Peres told CNN that a ground offensive might happen "quite soon". The army has called up about 40,000 reservists.
The military said its Iron Dome missile defence system had intercepted 21 of the 82 rockets fired on Wednesday, including three above Tel Aviv, three over Ashkelon and three over Ashdod.
The town of Hadera 100km (60 miles) north of Gaza, was hit with an M-302 surface-to-surface rocket, the furthest target so far reached.
Israel has carried out more than 230 air strikes since Tuesday, hitting nearly 600 targets as part of its operation Protective Edge.
Gaza health official Ashraf al-Kedra told AFP news agency that Israeli air strikes on Wednesday had killed four Palestinians in Shejaiya and two in Zeitun and two more in Beit Hanoun.
The head of the Palestinian Centre for Human Rights in Gaza, Raji Sourani, accused Israel of deliberately targeting civilians.
He told the BBC: "There is no safe haven in this place and Palestinian civilians are once again in the eye of the storm and are paying heavily."
Hamas said that all Israelis were now targets, accusing Israel of violating the Egyptian-brokered truce that ended exchanges in 2012.
The leaders of France and Germany condemned the attacks on Israel after speaking to Netanyahu.
Meanwhile, senior US officials urged "all sides to de-escalate the situation", a state department spokeswoman said.
However, Mark Regev, spokesman for Netanyahu, earlier confirmed that the situation was more one of escalation than de-escalation.
He told the BBC the Israeli army was acting to "dismantle Hamas's military machine".
"We don't want to have some sort of band-aid solution whereby we have a quick fix, a ceasefire and then we only have rockets on Israeli citizens next week," he said.
The leader of Hamas' political bureau, Khaled Meshaal, warned that Hamas would continue to retaliate and called on Palestinians to unite.
He also criticised what he described as the international community's lack of support for the Palestinian people.
"This war was forced upon us," he said in a televised speech on Wednesday.
Last month, Hamas and Abbas formed a unity government to end a major rift between factions in the West Bank and Gaza.
Israel suspended crisis-hit peace talks with the Palestinians in April in response to the announcement of the reconciliation deal.
Tensions rose last week with the murders of three young Israelis in the occupied West Bank and a Palestinian teenager in Jerusalem.
Israel says Hamas was behind the abduction and murder of the Israeli youths - a claim it denies.
A day after their funerals, the Palestinian youth was abducted in East Jerusalem and murdered. Police have arrested six Jewish suspects and say it seems the 16-year-old was killed because of his nationality.