"Our hand is extended towards an Israeli partner for making peace," said Abbas at the ceremony in the battered West Bank compound where his predecessor Yasir Arafat is buried. "We are seeking a mutual ceasefire to end this vicious circle."
"Peace can only be achieved by working together to reach a permanent status solution," he said, restating his support for a US-backed peace "road map" that calls initially for resistance fighters to be reined in while Israel eases its occupation.
In the latest bloodshed, Israeli occupation troops killed seven Palestinians in the Gaza Strip, including some armed men.
An Israeli girl aged 15 was critically wounded in an Israeli border town by a rocket attack, which Hamas said was launched in an "initial reaction" to Israel's Gaza raids. A three-year-old boy was also injured in a settlement in northern Gaza.
Wail al-Dahduh, Aljazeera's correspondent in Gaza said Israel was continuing its military operations in the area al-Zaytun area outside Gaza City.
"In the al-Zaytun area where the huge Israeli incursion is taking place, the Israeli tanks are still stationed at their posts.
"Special forces are taking positions on the roofs of some houses and firing at civilians and resistance fighters who are trying to resist Israeli tanks.
Hamas said it fired rockets on
Israeli towns and settlements
"Bulldozers are still carrying out immense razing operation.
"What is new is that the Israeli military helicopters have participated in firing at civilians and resistance fighters as well," he said.
The Israeli government said the incursion was a response to the rocket attacks on Israel and its settlements in Gaza.
"The real question is what kind of message did Abbas' words have for the various terrorist organisations," said Israeli Prime Minister Ariel Sharon's adviser, Dore Gold. "Clearly, they were insufficient."
Abbas (R) called for a "mutual
ceasefire" with Israel
Abbas wants an end to more than four years of Palestinian armed struggle so talks with the Jewish state can resume. His election last Sunday has kindled new hopes for Middle East peace in the era after Arafat's death on 11 November.
But Sharon, wary of Abbas's aim of co-opting resistance men rather than cracking down on them, said Israel would cut off ties after the resistance killed six Israelis in an attack on the Karni cargo terminal between Israel and Gaza on Thursday.
"I am sure that there would a positive response by Palestinians that is based on the desire to allow Abu Mazin (Abbas) to succeed internally and on the level of negotiations," said Nabil Amro, a member of the Palestinian Legislative Council (PLC) speaking to Aljazeera from Ram Allah.
"The problem is always the Israeli side which seeks to escalate the situation to contain Abu Mazin and blackmail him, particularity after the considerable international goodwill towards Abbas and the readiness to support him in his new political course.
"The problem is always the Israeli side which seeks to escalate the situation"
Palestinian Legislative Council member Nabil Amro
When asked about Abbas's call for a mutual ceasefire, he said, "Sharon has aborted the call yet he knows that Abbas has not started and that his contacts with all Palestinian factions have not developed fully.
"Abbas came to contain the state of violence and to begin a new political process," Amro said.
Abbas did not say in his speech how he planned to deal with the resistance. Nor did he refer to Israel cutting contacts.
"We don't see anything programmatic in what Abbas is saying. Israel will be very pleased in the future to get into other understandings with the Palestinians but right now they're the ones who have to halt the assault on us," Gold said.
Abbas is expected to meet
resistance groups in Gaza
Sharon and Abbas had been widely expected to meet soon to discuss security coordination in the run-up to Israel's planned pullout from Gaza this year and the possibility of resuming talks on Palestinian statehood.
Prospects for an end to bloodshed appeared to brighten when Sharon called Abbas this week. Israel had shunned Arafat, accusing him of fomenting violence, though he always denied it.
Abbas Gaza visit
Abbas has called for calm but has been defied by resistance groups, including some from his Fatah faction and Islamists. They launched repeated rocket and mortar attacks as well as Thursday's Karni border crossing assault.
Palestinian officials said Abbas was expected to go to Gaza this week and meet resistance groups.
Israel shut all Gaza border crossings after the Karni attack, suspending movement of Palestinians and goods in and out of the occupied territory.
Egyptian presidential spokesman Sulaiman Awad said the world must realise that Abbas "does not possess a magic wand with which he can stop the violence overnight".
Abbas said there would soon be talks on reshuffling the government that he inherited from Arafat, though he is keeping Ahmad Quraya as prime minister.