At least 20 people have died in the infighting, which has brought life in Gaza to a standstill. Eleven of the 20 died Tuesday.
The fighting came as a second cease-fire in as many days quickly collapsed, reports . The fighting has raised questions about whether a national unity government formed between Hamas and Fatah two months ago can survive.
In other developments:
The Palestinian clashes occurred on a major anniversary, as Palestinians were marking the Naqba, or catastrophe of Israel's creation 59 years ago, reports Berger.
Tuesday's fighting erupted when Hamas gunmen approached a training base used by Fatah forces that guard the Karni cargo crossing, officials said. The base was set up in part by an American security team sent to train Palestinians on how to check cargo and baggage.
The Hamas force attacked the base with rockets, rocket-propelled grenades and mortars, said Ahmed al-Kaisi, spokesman for the pro-Fatah Presidential Guard, which guards the crossing under an agreement with Israel. "We consider this a serious provocation and a crime committed in cold blood," al-Kaisi said.
When forces from another Fatah security unit raced to the scene to provide backup, they were ambushed by Hamas gunmen, witnesses said.
A jeep full of security men that came under fire veered off the road and crashed. Hamas forces then surrounded the vehicle and riddled it with gunfire, said one witness, who works in a nearby factory. "It was unbelievable. May God help us," said the man, who gave only his first name, Jamil, out of fear for his safety.
Hospital and security officials said eight men were killed in the ambush. After the incident, several bodies were seen strewn in the grass near the overturned jeep, as gunmen in pickup trucks nearby held machine guns in the air.
As the fighting raged, Israeli troops opened fire at two gunmen who approached the border, the army said. Palestinian officials said one man was killed. He was identified as a member of the Presidential Guard who apparently was trying to help his comrades against Hamas.
Hours after the Karni incident, another security officer loyal to Fatah was killed in a clash with Hamas gunmen in Gaza City, Fatah officials said.
Late Monday, Hamas and Fatah agreed to a new truce. But Tuesday morning, Palestinians awoke to the sound of gunfire throughout Gaza. Gunmen exchanged heavy gunfire at a security compound in Gaza City and a nearby junction was virtually empty even at rush hour.
Throughout most of Gaza City, Palestinians huddled scared in their homes for the second day, not going out to jobs or to school.
Salman Abu Arafeh said bullets flew through his apartment's windows during a shootout Monday, preventing him from reaching his shrieking children and wife in two separate rooms.
"I spent about four hours in the hallway unable to move an inch," said Abu Arafeh. "Right now, we are still in our apartment, but we are using our living room seats as an embankment when there is shooting. We crawl behind these seats to avoid flying bullets."
In the West Bank, Palestinian President Mahmoud Abbas called for the immediate implementation of a government security plan to halt the internal fighting.
The plan calls for rival security forces to operate under a joint command. The Palestinian interior minister who devised the plan resigned Monday in protest, saying both the Islamic militant Hamas and the Fatah movement of Abbas have undermined him.
Despite Abbas' pledge, it appeared unlikely the fractured Hamas-Fatah government has the will or clout to end the fighting and put all security forces under one command.
In a separate "Naqba" speech, Prime Minister Ismail Haniyeh of Hamas made little mention of the infighting, urging the Palestinians "to work together in order to protect our national unity government and make it succeed." Instead, he focused on the conflict with Israel.
"We have said that we are going to give the politics a chance, but we are not going to drop our weapons until the occupation evacuates our land and justice and security and peace prevail," he said.
While the Palestinian power-sharing agreement has reduced tensions, it has done little to halt a wave of kidnappings, carjackings, robberies and lawlessness gripping the Gaza Strip.
Meanwhile, Jordan's King Abdullah II told Olmert during their meeting in the seaside resort of Aqaba that Israel first had to take concrete steps to improve relations with the Palestinians.
"The king stressed first and foremost to Mr. Olmert that talking about new settlements or expanding existing ones is in contradiction with Israel's desire for peace," said Amjad Adayleh, the director of the information department at the Royal Palace.
Olmert told the king that such reports "were baseless," Adayleh said.
He added that Abdullah also "urged" Olmert to lift an economic blockade on Palestinians, making it easier for them to cross borders and "immediately unfreeze" all Palestinian funds held by Israel.