The attack happened late Sunday near an Israeli roadblock between Jerusalem and the West Bank town of Bethlehem. The military said the mother and a 9-year-old daughter were rushed to a hospital, while two other children were treated at the scene for cuts from broken glass.
In a phone call to The Associated Press, the Al Aqsa Martyrs' Brigades, affiliated with Palestinian leader Yasser Arafat's Fatah movement, claimed responsibility for the shooting.
CBS News Correspondent Robert Berger reports that Israel suspended further West Bank pullouts after the shooting attack. Officials say the Palestinian Authority must crack down on terrorism. However, Israel still plans to release more than 400 Palestinian prisoners later this week.
The attack came just hours after Israel rejected a proposal by Palestinian Foreign Minister Nabil Shaath for a permanent cease-fire. The deal would have halted attacks against Israelis, and not required the Palestinian leadership to crack down on militant groups as mandated by a U.S.-backed "road map" peace plan.
The shooting was the first Palestinian attack in the area since Israel turned Bethlehem back over to Palestinian security forces under terms of the peace plan, which calls on Israel to pull its forces out of Palestinian towns reoccupied during nearly three years of violence.
Israeli Defense Minister Shaul Mofaz said Israel would not hand over more towns to Palestinian control or consider releasing Palestinian prisoners until action was taken against Sunday's attackers. Shaath condemned the attack.
In other Israeli-Palestinian violence early Monday, a Palestinian man was killed while planting an explosive device on a road used by Israeli forces near the West Bank city of Tulkarem, Israeli military sources said. The forces spotted the man just outside the village of Faron and opened fire, fatally wounding him.
The Al Aqsa brigades identified the man as one if its members, 26-year-old Nihad Qasan, and accused Israel of assassinating him.
The Palestinian cease-fire offer was made in a meeting with Israeli Foreign Minister Silvan Shalom, officials on both sides said, but Shalom turned it down.
Palestinian Prime Minister Mahmoud Abbas refuses to order a crackdown on the militants, fearing a civil war. He prefers a negotiated end to violence, like the current truce.
Shaath said he told Shalom that further Israeli withdrawals from West Bank towns and other steps to allow Palestinians freedom of movement between towns could make it possible for the Palestinian government to negotiate a permanent cease-fire with the militants.
"Their reaction was that they were insistent that this is not enough, and they were insistent on the Palestinians dismantling the militant infrastructure," Shaath told The Associated Press.
A senior Israeli official, speaking on condition of anonymity, confirmed Shaath and Shalom discussed a permanent cease-fire, though the official said the Palestinians made an outright offer of a permanent truce. He said Shalom rejected the idea.
Main Palestinian groups called a temporary cease-fire on June 29. Since then, violence has dropped significantly, but Israel accuses the militants of using the truce to rearm and prepare for a new wave of attacks.
After the Sunday shooting, Israeli official Raanan Gissin renewed the call for a "sustained, targeted, effective operations against those involved in terror operations."
Israel published a list Monday of 342 Palestinian prisoners approved for release, including 183 inmates convicted of aiding militant groups or taking part in violent acts and 139 "administrative detainees" held without charge on security grounds.
They are among 440 prisoners whose release was approved by the government, officials said.
Media reports said the releases would begin Wednesday, but the list was published in advance to give Israelis time to appeal the release of specific prisoners.
Palestinians have pressed for prisoner releases since the start of their truce, though it is not part of the "road map" plan. The Israeli decision is not likely to win Palestinian praise, since the Palestinians have been demanding freedom for about 3,000 of the approximately 7,700 prisoners Israel is holding. Israel refuses to free Palestinians involved in terror attacks.
Hamas, in a statement faxed to The Associated Press in Gaza, said the group was growing impatient and called on Palestinians "to prepare themselves for confronting arrogance of that criminal enemy that denied the right of freedom for the heroic detainees."
Palestinian Prime Minister Mahmoud Abbas is due to meet later Monday with faction leaders in Gaza, Palestinian officials said. He will report on his recent talks in Washington and discuss the future of the cease-fire, as well as concerns over Palestinian prisoners and charges of Israeli truce violations.