The Palestine Liberation Organisation (PLO) has called for an end to attacks by militant groups against Israel.
Attacks cannot be allowed to continue, Sharon says
In its strongest such appeal since the death of Yasser Arafat, the PLO's top body "demanded halting all military acts that harm our national interests".
The call came hours after Israeli Prime Minister Ariel Sharon gave his troops free rein to crack down on militants.
Tensions have soared since Palestinian suicide bombers killed six Israelis at a Gaza Strip crossing late on Thursday.
In continuing violence, an Israeli tank shell killed a Palestinian woman and her son in Khan Younis refugee camp in southern Gaza on Sunday, Palestinian medics and witnesses said.
This follows the deaths on Saturday of eight Palestinians killed by Israeli troops during incursions into Gaza.
Two Israelis, including a seven-year-old, were also injured by Palestinian rockets.
In a statement, the PLO's decision-making executive committee said it gave its "full support to Abu Mazen's [Mahmoud Abbas] inauguration speech to stop all military acts that harm our national interest".
Mr Abbas - who was elected Palestinian president last Sunday and has also succeeded Arafat as PLO chairman - called for an end to violence on both sides and urged a resumption of peace negotiations with Israel.
He has said he will not use force against militants but try to persuade them to call a ceasefire.
The PLO embraces most Palestinian groups bar the Islamists.
Israel severed ties with the Palestinians following Thursday's truck bombing and gun attack at a Gaza-Israel crossing point.
Meanwhile Egypt's President Hosni Mubarak called on the Israeli leader to resume contacts with Mr Abbas.
On Sunday, the Israeli prime minister said he has given his troops a free hand to launch a crackdown on Palestinian militants.
"Despite the change in Palestinian leadership, we have yet to see them taking any action against terror," Ariel Sharon told his cabinet.
"The Israeli military and security apparatus have been instructed to take any action needed without restriction," Mr Sharon said on Sunday.
"These instructions will remain valid as long as the Palestinians fail to lift even a single finger."
Palestinian Foreign Minister Nabil Shaath condemned the announcement.
"At the same time that Abu Mazen says he will work hard to return to the peace track, Sharon declares a military escalation," he said, using the Palestinian leader's nickname.
Palestinian officials said Mr Abbas will visit the Gaza Strip this week in an effort to convince militant groups to stop attacks against Israeli targets.
But the BBC's James Reynolds in Jerusalem says Mr Sharon's latest move may complicate Mr Abbas' tactic of trying to reach a ceasefire through negotiation and persuasion.
Militant factions have indicated they will only stop attacks if Israel does the same.
Mr Sharon's comments to his cabinet suggest that that is unlikely to happen, our correspondent says.