Nabil Abu Rudina, the official spokesman for the Palestinian National Authority, made the remarks after the killing of six Israelis, Aljazeera reported.
"Israel should stop its escalation and military attacks and withdraw from Palestinian towns," Abu Rudina said.
Meanwhile, Israeli Prime Minister Ariel Sharon has frozen all official contact with the Palestinian leadership until further notice in response to Thursday’s bomb attack, one of his advisers said on Friday.
Thousands of Palestinians marched in the streets of Jabalya refugee camp in the Gaza Strip in what they described as a victory march.
The Friday march followed the killing of the Israelis by fighters who mounted their strongest challenge yet to Abbas and his call for resistance groups to lay down their arms.
The march was organised by resistance groups and was seen as a sign of grassroots support for their defiance of Abbas and the battle against occupying Israel.
Resistance fighters march in
Three Palestinians were also killed during the bombing and shooting assault at al-Mintar (Karni), the main cargo crossing between Israel and Gaza, late on Thursday.
Three groups claimed they carried out the attack: Hamas, the Popular Resistance Committees and al-Aqsa Martyrs Brigades, an armed wing of Abbas' Fatah movement. Israel signalled it would weigh its response to the bombing carefully to avoid weakening Abbas.
"We will continue to chase you and disrupt your sleep until you leave the land you occupied," the resistance groups said in a statement.
There was no comment from Abbas, who won last Sunday's election for a successor to Yasir Arafat and who is due to be sworn in on Saturday.
The new leader has urged a ceasefire after four years of bloodshed during the second intifada (uprising) to allow for the resumption of talks with Israel on peace and Palestinian statehood.
"We will continue to chase you and disrupt your sleep until you leave the land you occupied"
Resistance groups' statement
The ceasefire call has been rejected by resistance groups who argue that Israel must also abandon its military offensive. Abbas, also known as Abu Mazin, hopes to co-opt rather than confront the resistance groups.
Palestinian Labour Minister Ghassan al-Khatib said he did not see the al-Mintar assault as a challenge to Abbas but rather as a message from the fighters that "if Israeli attacks continue, the reaction to these attacks will continue".
Following the attack, Israel announced it was indefinitely closing three border crossings to the Gaza Strip.
Israeli Defence Minister Shaul Mofaz said the crossings would remain closed until further notice, Aljazeera reported.
The al-Mintar crossing, a major lifeline for supplies to 1.3 million Palestinians in Gaza, was shut down immediately after Thursday's attack; while the second crossing at Erez on the northern edge of the Gaza Strip was closed on Friday.
The third crossing, Rafah, on the border with Egypt has been closed for five weeks.
The closing of the three crossings effectively isolates the Gaza Strip from the rest of the world.
Change of tone
Israeli Justice Minister Tzipi Livni said the army would have to take action to prevent further Palestinian attacks. Israel's military commander in Gaza, Brigadier Aviv Kochavi, pledged ongoing operations against fighters.
But in a change of Israel's tone towards the Palestinian Authority after years of accusing Arafat of instigating violence, Livni said: "We must try to strengthen [Abbas] as a leader, assuming that at some time or other he will be able to take control of the terror organisations."
Israel has talked of strengthening
president-elect Abbas (R)
Israeli cabinet minister Matan Vilnai said Abbas' election and Israel's planned pullout from Gaza later this year presented a historic opportunity for peace.
"We have Abu Mazin - Arafat has left us at last. Abu Mazin speaks a different language," Vilnai said.