The flare-up, sparked by anger in Gaza over the death from cancer of a Palestinian held by Israel, included Israel's first air strike on the Hamas-run coastal enclave since the truce.
Confrontations spread to the occupied West Bank, where Israeli forces clashed with dozens of Palestinian protesters in the city of Hebron, where Maysara Abu Hamdeya who died in jail on Tuesday aged 64, is due to be buried on Thursday.
Troops fired teargas and rubber bullets at youths throwing stones and petrol bombs; Reuters journalists saw several protesters escorted away with injuries. The Israeli military said a rock had also struck one of its officers in the face.
Some 4,600 Palestinian prisoners declared a hunger strike for three days in protest at Abu Hamdeya's death, accusing the authorities of poor medical treatment. Food trays were returned untouched on Wednesday, an Israeli prisons official said.
In West Bank towns, some shops were shuttered in solidarity.
The Gaza frontier fell quiet by evening and Israel and Hamas appeared to be weighing carefully their next moves; four months of relative calm has enabled Palestinians in Gaza to rebuild and Israelis near the border to live without sirens and rockets.
Two rockets fired from the Gaza Strip had struck southern Israel in a morning attack on Wednesday, causing no casualties, the Israeli military said. Hours earlier its planes had targeted "two extensive terror sites" in the north of the territory.
Israel launched the air strike after three rockets landed on Tuesday. An al Qaeda-linked group, Magles Shoura al-Mujahadeen, claimed responsibility for the attacks on both days, saying it was responding to the death of Abu Hamdeya, who was jailed for life in 2002 over a planned bomb attack on a Jerusalem cafe.
Tuesday was the third time since the November truce that rockets from Gaza had struck southern Israel. But with a new government and defence minister now in place after weeks of coalition-building since a January election, Israel seems keen to show resolve, putting the onus on Hamas to curb militants.
"(Israel's armed forces) decided to attack overnight in order to signal to Hamas that we will not suffer any strike on the south. And any shooting will meet a response, in order to restore quiet for the south soon," Brigadier-General Yoav Mordechai, the chief military spokesman, said on Army Radio.
"I assess that Hamas has no interest in seeing the situation deteriorate," he said. "Our goal is to maintain the quiet."
SYRIA SPILLOVER
Spillover from the civil war in Syria - mortar and machinegun fire toward Israeli troops in the Israeli-occupied Golan Heights - has also heightened Israeli unease.
"We will absolutely not allow any sporadic fire toward our citizens and our forces," Defence Minister Moshe Yaalon said in a statement, referring to both Gaza and Syrian frontiers.
Israeli tanks fired at a Syrian post on Tuesday, though it was unclear whether rebel or government forces were manning it.
Hamas, an Islamist group close to the Muslim Brotherhood now ruling neighbouring Egypt, has cracked down on hardline Salafist rivals it sees as jeopardising its control of the Gaza Strip.
But the death of Abu Hamdeya has touched a nerve among the wider Palestinian populace, which regards those in Israeli jails as heroes in the fight for statehood.
Israel has denied negligence in his treatment.
Commenting on the violence in Gaza, Richard Serry, the U.N.'s special coordinator for the Middle East peace process, said it was of "paramount importance to refrain from violence".
He said in a statement that renewed violations of the ceasefire threatened to unravel Egyptian-brokered understandings that included an easing of Israel's blockade on the enclave.
Egypt mediated the November truce after fighting in which some 170 Palestinians and six Israelis were killed. Israel had launched that Gaza offensive, as it did a bigger campaign in 2008-09, with the declared aim of ending rocket fire.
Hamas seized control of the Gaza Strip from Western-backed Palestinian President Mahmoud Abbas's Fatah movement in 2007 after winning an election a year earlier. Palestinians want to establish a state in the enclave along with the West Bank and East Jerusalem, territories Israel captured in a 1967 war.
