A fierce gunbattle broke out between Hamas and Fatah militants in Gaza City early Friday, underscoring the fragility of a two-day old truce that had largely ended factional violence there.

The street battle erupted when Hamas militiamen tried to free two kidnapped militants, including a senior member of the Islamic group. It died down after 20 minutes as Muslim clerics and other mediators worked to restore the cease-fire. Nobody was hurt despite the battle's intensity, health officials said.

Hamas said its fighters exchanged fire with Fatah-affiliated militants behind the abductions. The fight quickly spread, drawing in guards outside the residence of Palestinian President Mahmoud Abbas of Fatah, and Hamas militiamen guarding the home of Foreign Minister Mahmoud Zahar of Hamas Zahar. Abbas was not in Gaza at the time.

Meanwhile, Palestinians stepped up rocket attacks on Israel, including one that veered off course and hit a Gaza home, injuring a 2-year-old Palestinian boy sleeping in his bedroom, officials aid.

Six other rockets landed in Israel, but nobody was hurt. The barrage threatened a separate cease-fire between Israel and the Palestinians that ended months of Israeli military activity in the Gaza strip.

Click here to go to FOXNews.com's Mideast Center.

A minister in Olmert's Cabinet said it was time to call off the cease-fire.

"Enough restraint," Binyamin Ben-Eliezer told Israel Radio. "Israel is many things, but a suicidal state isn't one of them."

A week of factional violence in Gaza has killed 16 people and left dozens injured across Gaza before the truce took effect Tuesday night.

Hamas blamed the Thursday night kidnappings on a clan affiliated with Fatah that was trying to avenge the deaths of two its members in an earlier round of fighting.

In Friday's battle, gunmen on rooftops fired at others in the streets. The presidential guard took up defensive positions behind newly built walls of sandbags and barriers of cement blocs outside Abbas' residence.

Hamas officials said the Fatah gunmen shot at Zahar's home.

One witness said several rocket-propelled grenades were also launched. Residents said they put their children in bathtubs for protection against stray bullets. Others tucked themselves in corners for safety.

The militant group Islamic Jihad claimed responsibility for some of the rockets that landed in Israel, including one that hit a community center the southern town of Sderot. The army said the rocket caused some damage but nobody was hurt.

There was no immediate claim of responsibility for the attack that struck the Gaza home. In the past, similar cases of Palestinians being hurt by Palestinian rockets have led to backlashes against militant groups, whose attacks against Israel are generally supported by the public.

The boy, Samir al-Masri, suffered two broken legs, said Dr. Said Judeh of Kamal Adwan hospital. The boy's 4-year-old sister and 3-year-old brother were lightly wounded by shrapnel, said their uncle, Jad al-Masri.

Abbas, a moderate, has repeatedly called for an end to rocket fire, saying they only invite harsh Israeli retaliation.

In the West Bank town of Ramallah, Abbas said he hoped to hold a long-awaited summit with Olmert by the end of the year.

"We always showed our willingness to hold this meeting with Olmert, and it's no secret that we hope it will take place before the end of this year," Abbas said at a news conference with the visiting Italian foreign minister, Massimo D'Alema. "There is progress in preparations for this meeting."

The two leaders have repeatedly expressed readiness to meet for what would be their first summit. But preparations have bogged down amid disagreements over the agenda.

Abbas wants Israel to promise to release hundreds of Palestinian prisoners. Olmert has ruled out a prisoner release until Hamas-linked militants free an Israeli soldier they captured last June. Olmert's spokesman, Jacob Galanti, said he was not aware of firm plans for a meeting.

Click here to go to FOXNews.com's World page.