One raid on Tuesday was against a building belonging to the Fatah movement of Palestinian Mahmoud Abbas in Bait Hanun in the north of the Gaza Strip. The building was damaged but no casualties were reported, witnesses said.
The second attack was on a building belonging to resistance group Islamic Jihad at Rafah in the south of the strip. Although the building was badly damaged, no casualties were reported, witnesses said.
The latest flare-up came after Israeli troops shot dead an Islamic Jihad commander in the occupied West Bank, the most senior Palestinian fighter killed since the start of a ceasefire in February.
Islamic Jihad fighters fired at least three rockets at Israel from the Gaza Strip in response, but caused no casualties.
Witnesses said one hit a mourning tent for a dead Palestinian, while the Israeli army said two landed near the border fence with Israel.
Resistance groups stopped such attacks last month after a flare-up in violence in which Israel killed several armed men after similar rocket salvos.
Abbas: Escalation of violence
threatens security efforts
But Islamic Jihad vowed to avenge Israel's killing of Luai Assadi, 26, a top West Bank leader of Islamic Jihad who was accused of masterminding bombings that killed 10 Israelis since the truce was declared in February.
Islamic Jihad members in northern Gaza said they fired 25 rockets into Israel in retaliation. There were no casualties.
The Israeli occupation army said several landed in open fields in Israel and that they responded with artillery fire into Gaza.
Israeli warplanes carried out mock raids over Gaza City, breaking the sound barrier and causing panic among the population in the strip, in response to the rocketing, Aljazeera learned.
The renewed violence threatened to unravel the frayed ceasefire and undermine hopes that Israel's Gaza pullout last month, after 38 years of occupation, could revive peacemaking.
The Israeli army said soldiers raiding the town of Tulkarim targeted Assadi and another fighter, Majid al-Ashkar, killed on Sunday, because they had been planning further attacks.
Palestinian President Abbas' office said in a statement the West Bank killing marked an escalation in violence that threatened to undermine Abbas' efforts to bring calm and security.
Although Islamic Jihad had declared its commitment to maintain "calm" until the end of the year, its Gaza-based leader Muhammad al-Hindi said on Monday: "Calm does not deprive the Palestinian people from responding to crimes."
"We will not stand handcuffed while the blood of our fighters is being shed... Let calm go to hell"
Islamic Jihad statement
Shortly before launching the rocket salvo, the group's military said in a statement: "We will not stand handcuffed while the blood of our fighters is being shed... Let calm go to hell."
Israel has said it has the right to target "ticking bombs".
Israeli officials say Assadi was behind two bombings this year, one that killed five people at an Israeli shopping mall in the coastal city of Netanya in July and another that killed five Israelis outside a Tel Aviv nightclub in February.
Army Colonel Aharon Haliva, commander of the force that entered Tulkarim, said troops surrounded a house where Assadi was hiding and killed him when he fired on them as he tried to escape. A soldier was slightly hurt.
The army said Assadi had planned to send a bomber into Israel in coming days.
At the start of the raid, soldiers riddled a car with gunfire, killing Ashkar, 26. He was connected to both Islamic Jihad and al-Aqsa Martyrs Brigades, affiliated to Abbas' Fatah group.
Haliva said troops killed Ashkar after he shot first, slightly wounding a soldier. Palestinian witnesses said he never fired.
The army has made frequent raids into Tulkarim and other major West Bank cities and towns during a five-year-old Palestinian uprising.
Prime Minister Ariel Sharon has vowed that Israel will never give up large West Bank settlement blocs where about 245,000 Jews live amid 2.4 million Palestinians.
Israel evacuated 8500 settlers from Gaza last month.