The New York Times said Tuesday's violence was some of the most intense in the week-old crisis between Palestinian militants and Israel, despite word a cease-fire was close to being reached.
More than a dozen people were killed in an aerial strike on a suspected rocket-launching site near al-Shifa hospital in Gaza. Israeli naval vessels also fired on the Gaza coastline.
An Israeli soldier and a civilian military contractor died Tuesday in rocket attacks by militants near the the Gaza border. Palestinian rockets hit Beersheba and Ashdod. Rockets were also fired toward Tel Aviv and Jerusalem, but neither city was hit, the newspaper said.
Essam el-Haddad, Egyptian President Mohamed Morsi's top foreign affairs adviser, said Israel and Hamas were "very close" to a cease-fire agreement, The Times reported. Israel's Channel 2 television, however, said negotiators needed more time.
U.S. Secretary of State Hilary Clinton arrived in Israel late Tuesday and immediately began talks with Israeli Prime Minister Binyamin Netanyahu. U.N. Secretary General Ban Ki-moon also arrived in Israel Tuesday.
Netanyahu's office said Israel is giving more time to diplomacy before starting a ground invasion of Gaza.
"As you know, we seek a diplomatic unwinding to this through the discussions of cease-fire," Netanyahu said in a statement. "But if the firing continues, we will have to take broader action and we won't hesitate to do so."
Israel Radio, quoting unnamed officials close to the truce talks, said earlier Tuesday the Jewish state will agree to a cease-fire it hopes will last for at least two years, enforced by Israel, the United States and Egypt. After two years and in the event Israel comes under attack by Hamas in Gaza, Israel will be forced once again to act against the terrorist infrastructure in Gaza, the report said.
Ban has urged all sides to "halt fire immediately."
"Further escalating the situation will put the entire region at risk," he said at a news conference in Cairo before heading for Israel.
German Foreign Minister Guido Westerwelle, also visiting Israel, met with Israeli President Shimon Peres and Netanyahu. He told the Israeli prime minister Israel has the right to defend itself against rocket attacks but expressed concern over the repercussions of a possible ground offensive, Israel Radio said.
Arab League Secretary-General Nabil al-Araby and 16 foreign ministers from the league's member states were to arrive in Gaza, joined by Turkish Foreign Minister Ahmet Davutoglu. Iran's Foreign Minister also announced plans to visit Gaza in the coming days, the report said.