There were no casualties in either attack, which came just as as Israel-Palestinian peace talks were set to begin in Jerusalem, The New York Times reported.
A statement from the Israeli military said Hamas was behind rocket fire launched at civilians living in the Sha-ar HaNegev regional council Tuesday, The Jerusalem Post reported.
"This is an absurd situation that would not be tolerated anywhere else in the world," Lt. Col. Peter Lerner, a spokesman for the military, said in a statement. He said the military "is charged with, and will continue to operate in order to safeguard Israel's civilians and combat terror and its infrastructure in the Gaza Strip."
Envoys from both sides prepared for Middle East peace talks hours after Israel freed 26 Palestinian convicts and approved 890 new homes in a disputed part of Jerusalem.
Israeli Justice Minister Tzipi Livni, Israel's chief negotiator and a proponent of establishing a Palestinian state alongside Israel, and Palestinian Authority chief negotiator Saeb Erekat, who negotiated the 1993 Oslo Accords with Israel, were to meet at the U.S.-sponsored talks in Jerusalem.
U.S. special envoy for Israeli-Palestinian negotiations Martin Indyk and Frank Lowenstein, his deputy, were expected to "help facilitate" the talks, the U.S. State Department said.
After the Jerusalem talks, the negotiators promised to hold another session in Jericho on the West Bank. The date for that session was not immediately announced.
Further meetings were expected to be held every few weeks.
Israel, the Palestinian Authority and the United States have committed to nine months of negotiations to reach a comprehensive peace agreement that would produce "two states for two peoples" in territory known as the British Mandate of Palestine from 1920 until Israel's 1948 creation.
Israel and the Palestinian Authority met for preliminary talks in Washington two weeks ago after U.S. Secretary of State John Kerry made resurrecting peace talks a key priority.
The talks had been stalled for three years, in large part over growing Israeli settlements and Palestinian concerns about their repercussions on the viability of a future Palestinian state.
On the eve of Wednesday's talks, Israeli media reported the Israeli Interior Ministry gave final approval to 890 new apartments in contested East Jerusalem.
The approval was published Monday but not reported until late Tuesday.
News of the housing units followed the Israeli Housing Ministry's Sunday announcement it approved construction of 1,200 apartments in other parts of Jerusalem and the occupied West Bank.
The 890 units are to be built in Gilo, a large, mostly Jewish residential area in southwestern East Jerusalem. Gilo is widely considered an Israeli settlement because it's one of five "ring neighborhoods" Israel built on land occupied and annexed by Israel after the 1967 Six-Day War.
The international community, including the United States, regards Israeli settlements as illegal.
Kerry Tuesday repeated longstanding U.S. policy "with respect to all settlements is that they are illegitimate."
Israel disputes this.
In the past week, Jerusalem approved or advanced nearly 3,200 units of housing on land it seized during the war, around Jerusalem area and in isolated parts of the West Bank, the Los Angeles Times said.
An Interior Ministry official told The New York Times Tuesday the publication of the ministry's final approval of the Gilo apartments was "just a procedure."
The Housing Ministry and Israel Land Authority must still evaluate construction bids for the housing, the official said, and groundbreaking could be months or more into the future.
But the timing of the news angered Palestinians just as the peace talks were to resume, the Times said.
The timing also came shortly before Israel released the first 26 of 104 Palestinian prisoners it agreed to free to bring Palestinians back to the negotiating table.
The release was part of a phased freeing of the prisoners, who are serving at least 20 years for attacks on Israelis.
The convicts were released around 1:30 a.m. Wednesday, a move widely seen as timed to reduce news coverage and dampen Palestinian arrival ceremonies.
They had been transported across checkpoints in vans with tinted windows to avoid the semblance of a victorious release, Ynetnews reported.
Eleven were released in Ramallah and 15 were freed in Gaza.
Despite the timing, hundreds of Palestinians greeted the men like returning war heroes.
"We welcome our brothers who have left the darkness of prison into the light of freedom and tell them they are the first but there are other brothers who too will leave soon," Palestinian Authority President Mahmoud Abbas said in Ramallah.
"We shall not rest until they are all with us," he said.
After the welcoming ceremony, the men sped off to their West Bank homes in convoys, photos taped to the car windows and horns honking, The New York Times said.
To Palestinians, the men are freedom fighters and national heroes who were imprisoned for striking against the Israeli occupation of their homeland.
To most Israelis, the men are terrorists and criminals who killed Israeli civilians, including women, children and, in one case, a 67-year-old Holocaust survivor found bludgeoned to death in 1994.
Most of the freed prisoners were serving life sentences.
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