Israeli jets also conducted several supersonic booms above the Gaza Strip.
Israel confirmed the Khan Yunis attack, which targeted a Fatah cultural centre, and follows rocket fire on Israeli territory from the Gaza Strip.
Earlier, Palestinian militants kidnapped an Italian peace activist and detonated explosives at the UN's beachfront social club after ending a year-long truce.
The targeting of both foreigners and Israelis in a series of rocket attacks served as a double blow to the crumbling authority of Palestinian leader Mahmud Abbas, who said armed groups are making a serious mistake by declaring an end to the "cool down."
Mr Abbas has been a consistent critic of rocket attacks and has urged the factions to stop regarding themselves as above the law.
But rather than reverse a tide of lawlessness since Israel left Gaza in September, Mr Abbas has presided over a worsening of the chaos that prompted a call to order from UN Secretary General Kofi Annan.
Italian kidnapped
Just a day after the release of three Britons who were kidnapped near Gaza's border with Egypt, an Italian peace activist was briefly kidnapped on Sunday in Khan Yunis.
Alessandro Bernardini had been part of a group of around 20 Italians on a mission designed to show solidarity with the Palestinian people.
But shortly arriving in Khan Yunis, he found himself being bundled into a vehicle by masked by gunmen who promptly sped him away.
Atif Alean, head of operations in the preventive security branch, said that the kidnappers and Mr Bernardini had been traced several hours later to a house near Khan Yunis that was subsequently surrounded.
"The kidnappers opened fire against us. Our forces responded in the direction of the shooting but the kidnappers ran away from the area," he said.
A weary-looking Mr Bernadini told reporters that he harboured no bitterness.
"I will never change my idea about the Israeli occupation of Palestine... I am with the Palestinian people," he said.
The Palestinian Authority is trying to attract foreign investment and aid to Gaza but the kidnappings are serving to scare people off.
All but a handful of the UN's foreign staff have left Gaza but the organisation was still the overnight target of gunmen who stormed its club on the shores of the Mediterranean, beat up a lone security guard on duty and then detonated a number of hand grenades.
A UN source said that the club, the only place that serves alcohol in the devoutly Muslim territory, had not been open for New Year celebrations as only three international staff remain in Gaza.
Mr Annan's office put out a statement condemning the attack.
"(The secretary general) calls on the Palestinian Authority to take all possible steps to bring the perpetrators to justice, prevent such attacks from recurring, and ensure law and order," the statement said.
Despite repeated pledges, Mr Abbas has failed to tackle the lawlessnesss of Gaza where members of armed factions, operating in the name of "resistance" to Israel, act above the law.
Truce days numbered
The main factions had signed up to a truce he brokered at the start of 2004, agreeing to "cool down" their campaign of attacks against Israel at least until the end of the year.
Mr Abbas had strong hopes that the militants would agree to extend the truce but a recent upsurge in rocket attacks, prompting Israel to reassert control over parts of the northern Gaza Strip, had shown its days were numbered.
Confirmation that the factions no longer feel bound by the so-called "tahdiya" came with statements from three groups which claimed credit for a series of rocket attacks into Israel.
The Al-Aqsa Martyrs Brigades and the armed wing of Islamic Jihad said in a joint statement they had fired two rockets at the southern Israeli town of Sderot while the Popular Resistance Committees said it had fired rockets at army posts and at a kibbutz in Israel.
A military spokeswoman confirmed three rockets landed on southern Israel but without causing any injuries.
The armed wing of Hamas, responsible for the majority of attacks during the five-year uprising, also confirmed it was ending its adherence to the truce.
Mr Abbas criticised the decision, saying "those who speak of an end to the truce are committing a grave error."
"I don't see any reason to end (the truce), despite multiple violations by Israel," he was quoted as saying on a visit to Abu Dhabi.