Incursion 'a massacre'
Israel's incursion came a week after Bush said he wanted a peace deal between the Israelis and the Palestinians by the end of his presidential term at the end of 2008.
Hamas officials blamed Bush's presence in the region for the violence.
Ehud Olmert, the Israeli prime minister, has reportedly ordered a series of such "sharp and short" incursions, into Gaza and the West Bank.
Abbas said on Tuesday: "What happened today is a massacre, a slaughter against the Palestinian people.
"Our people cannot keep silent over these massacres. These massacres cannot bring peace."
Peace bid 'damaged'
He said the Gaza operation, in which Hussam al-Zahar - the son of Mahmoud al-Zahar, a former Hamas foreign minister - was also killed had severely damaged the peace efforts relaunched by Bush in the US city of Annapolis less than two months ago.
Related link

Palestinians yearn for unity

Israel intransigent towards Bush visit

It is the second of al-Zahar's sons to be killed by Israel.
Al Jazeera's Jacky Rowland, reporting from Gaza, said that the death toll was likely to rise.

She said: "It's not just the destruction and devastation, but the effect this operation will have on peace talks."
The US president had started his tour last week by visiting Israel and emphasised America's bond with Israel.
Negotiations 'threatened'

Ahmed Qureia, the chief Palestinian negotiator, said that if the violence continued it would render the negotiations "meaningless".
Taher Nunu, a Hamas spokesman, said: "What is clear is that there is an Israeli plot to destroy the whole region.
"President Bush gave the green light to such aggression and such terrorism."
He said: "To all the Arab countries, to the custodian of the two holy mosques [King Abdullah of Saudi Arabia], Arab leaders and heads of states, we would like to tell them that they have to act immediately in order to put an end to this aggression."
Israel said they were engaging in an operation "against terror threats".

Since Annapolis, at least 115 Palestinians have been killed by Israeli fire in Gaza, according to an AFP count.

Suspension of talks urged 
The Israeli assaults on Gaza have sown further discord between Israel and the Palestinians, who are also angry over the expansion of Jewish settlements on occupied land in the West Bank, despite negotiation attempts.
Meanwhile, al-Zahar has called for the suspension of Israeli-Palestinian talks initiated by Bush during his visit to the region last week.
Al-Zahar said the Palestinians would retaliate
in the way Israel understands [AFP]
He said: "We believe that this Zionist escalation is the result of Bush's visit and a natural result of the cover supplied by Bush to the Israeli occupation authorities to go forward in their escalation and aggression against our Palestinian people, particularly in Gaza Strip.

"We will retaliate in the way they understand."
An Ecuadorian who had been working in a field on an Israeli kibbutz, or farming community, was shot dead by a Palestinian during the fighting.
The deaths follow Monday's missile attack by Israel near the Gaza home of Ismail Haniya, the Hamas leader, which killed three Palestinians.
Tuesday's deaths bring to 6,067 the number of people killed since the start of the second Palestinian uprising in September 2000, the vast majority of them Palestinians, according to a news agency tally.