Palestinian militants in the Gaza Strip fired six rockets at the Israeli town of Sderot, slightly wounding a 10-year-old girl and damaging a house.
There was a loud boom and people began running, said a witness.
Palestinians said the rocket attack was retaliation for Israel's assassination Thursday of a senior Islamic militant. The rocket attack is bound to spark more Israeli raids, reports CBS News Correspondent Robert Berger.
Despite the violence, with his top diplomat heading to the region, President Bush is sounding more optimistic that progress is in the cards, reports CBS News White House Correspondent Mark Knoller.
"Of course we're going to make progress. Yes, we'll make progress; absolutely," Mr. Bush said. "And the reason why we'll make progress is that the Palestinian Authority has now got a leader in the prime minister who has renounced violence," referring to Palestinian leader Mahmoud Abbas.
There's much less optimism in the Middle East than in Washington, reports Berger, because the "road map" peace plan has already run into trouble.
The main problem is the road map's demand that the Palestinians dismantle terrorist groups. The Palestinians say that would lead to civil war, and first, they want Israel to ease up on military action. Israel says it will offer no concessions until the Palestinians crack down on terror.
Israeli Prime Minister Ariel Sharon, however, on Friday praised Abbas, his new Palestinian counterpart, as a "partner" for peace and said he is ready to renew peace talks with Syria without conditions.
However, "without preconditions" means Israel wants to come to the negotiating table without making any commitments to a withdrawal from the strategic Golan Heights.
In the past, Syria has demanded an Israeli commitment to a full withdrawal as a precondition to peace talks, so chances for renewing those talks still appear slim.
One of the homemade Qassam rockets fired from Gaza struck a street in Sderot, a Negev Desert town, spraying debris that lightly injured a girl, who was taken to a hospital, police said. Three other people were treated for shock.
The rockets struck just a few miles from Sharon's sheep ranch. Militants have fired dozens of the rockets into Israel in recent months. The attacks have caused little damage and few injuries, but Israel considers them a provocation.
In the Gaza Strip town of Deir el-Balah, Israeli army bulldozers demolished eight homes and damaged another two, making 45 people homeless, the mayor said. The homes are close to the Jewish settlement of Kfar Darom, where a Palestinian blew himself up in a car late Thursday as he rammed into a tank.
The attacker was killed, and the Al Aqsa Martyrs' Brigade, a militia linked to Yasser Arafat's ruling Fatah movement, claimed responsibility. Abbas, who is a senior Fatah leader, has denounced such violence.
The peace plan envisions a final peace agreement, including the creation of a Palestinian state, by 2005. It is to be launched with statements by both Israel and the Palestinians, with each saying it recognizes the other's right to exist in peace and security.
Palestinian Cabinet Minister Saeb Erekat said Friday he hopes the declarations can be made during Powell's two-day visit, which begins Saturday. "The Americans can help both sides to produce the statements required to kick off the process," Erekat said.