The al-Aqsa Martyrs' Brigades and the armed wing of Islamic Jihad said in a joint statement that they fired two rockets at the southern Israeli town of Sderot at 4.15am (0215 GMT). There were no reports of casualties.
The Popular Resistance Committees said in a separate statement sent to AFP's offices in Gaza City that it had fired rockets at army posts and at a kibbutz in Israel on Sunday.
An Israeli military spokeswoman confirmed that rockets had been launched.
"Several launches were identified but nothing landed inside Israel," she told AFP.
The armed factions had been observing an increasingly shaky truce until midnight on Saturday but decided to abandon the agreement, negotiated by Mahmoud Abbas, the Palestinian president, in March.
The Popular Resistance Committees' statement said its attacks were in response to Israel's recent imposition of a "no-go" zone in northern Gaza, intended to prevent rocket attacks.
Two Palestinians were killed by
Israeli gunfire in Bait Lahiya
"We confirm that we will fight the enemy everywhere and we will regain control of northern Gaza for the people," it said.
'Cooldown is over'
The statement by Islamic Jihad and al-Aqsa said the attacks "confirmed our obvious position that the cooldown is over".
"The Zionists will have no security if they continue these attacks against our people and we will not sit with our hands tied."
A Hamas spokesman speaking to Aljazeera said that as the world welcomed in the new year, Palestinians bid farewell to 2005 by receiving more bodies and witnessing more bloodshed.
Hamas's Mushir al-Masri said
Israel is not interested in peace
Two Palestinians were killed by Israeli gunfire in the town of Bait Lahiya in the northern Gaza Strip on Sunday.
Mushir al-Masri, a Hamas spokesman, said: "This incident proves to the world that the Zionist enemy does not adopt an approach of calm or a language of peace.
"It only knows how to carry out more crimes and practice more terrorism against our Palestinian people."
Al-Masri confirmed that, according to the Cairo agreement, the period of calm ended on Sunday.
"The period of calm was also based on some conditions, such as the halt of Israeli aggression against Palestinians and release of Palestinian detainees," he said.
"However, the Zionist enemy was not committed to these conditions, as more than 150 Palestinians were killed, more than 1000 injured and more than 3500 detained during this period of calm," he added.
"The Zionist enemy was not committed to these conditions, as more than 150 Palestinians were killed, more than 1000 injured and more than 3500 detained during this period of calm"
Al-Masri said a renewal of a period of calm will depend on Palestinian talks.
"The final position will be decided according to the welfare of the Palestinian people," he said.
West Bank rocket
Also on Sunday, an Israeli security source said Palestinian fighters have made their most successful attempt yet to fire a makeshift rocket into Israel from the West Bank, Reuters reported.
Military censors delayed publication of the incident for three weeks, reflecting concern in Israel that armed Palestinian groups could target its main towns and cities with rockets from the occupied West Bank.
Until now, Palestinians have fired the rockets only from the Gaza Strip, which is not so close to Israel's major population centres.
The security source said that the rocket fired from the northern West Bank was a cruder version of those launched in Gaza. It fell just short of the boundary between Israel and the West Bank, causing no damage or casualties.