Shortly after the announcement was made, the head of the armed branch of another Palestinian radical movement, Islamic Jihad, was killed by the Israeli army in the West Bank town of Nablus.
Palestinian security sources said Hamad Abu Sharif, chief of the Al-Qods Brigades, was killed.
An Israeli military spokesman confirmed an armed man was killed.
"Soldiers operating in the old town opened fire on armed men killing one of them," he said.
Earlier two members of a Palestinian militant group, the Popular Resistance Committees, had been killed in an Israeli air strike.
Israeli sanctions
The attacks come as the Israeli cabinet announced it will impose strict sanctions on the Palestinian Authority, just as newly elected Hamas leaders were sworn into parliament.
Israel’s acting Prime Minister Ehud Olmert said the cabinet will withhold millions of dollars of customs revenue it collects on behalf of the Palestinian Authority, now dominated by the radical group apparently intent on Israel’s destruction.
President Abbas said Israel’s decision to permanently halt the monthly transfers of about $US50 million ($A67.72 million) will plunge the government into dire financial straits.
"Unfortunately, the pressures have begun and the support and the aid started to decrease... therefore we are currently in a real financial crisis," the Palestinian leader told reporters in Gaza.
"We hope we can surmount this crisis month by month," he said.
But in addition to the sanctions, Israel's biggest ally, the United States, has asked the Palestinian Authority to return a further $US50 million aid to ensure it does not reach Hamas.
Peace talks urged
Mr Abbas is set to meet Hamas leaders soon to discuss forming a unity cabinet, and will urge the government to recognise past peace deals with Israel and commit to pursuing statehood through talks.
"I would like to listen to them directly and to know what their positions and opinion are," he said.
Mr Abbas's long-dominant Fatah faction was crushed by Hamas in January elections and holds 74 seats in parliament.
Ismail Haniyeh, Hamas's choice for prime minister, said earlier that "everything will be on the table" during the talks.
"We want to avoid any sharp debate, especially while the (Israeli) occupation refuses to recognise Palestinian rights and refuses to recognise the agreements signed with the (Palestinian) Authority," Mr Haniyeh said.
Tougher sanctions avoided
Facing international pressure, Israeli officials backed down after earlier threatening to slap the Palestinian Authority with tougher measures in an attempt to weaken Hamas.
The measures would have included a ban on the entry of Palestinian workers into Israel, several thousand of whom are allowed in daily, as well as a tightening of restrictions on the movement of Palestinians between the Gaza Strip and the occupied West Bank.
Both the US and the European Union do not want to push the Palestinian Authority to collapse or to seek funding from states such as Iran, but have also threatened to halt aid.
Washington and its allies have urged nations to boycott Hamas, unless it disarms and recognises the Jewish state and past peace deals.
However Russia said it will invite Hamas leaders for talks in Moscow.
In a statement, the Israeli government also called on international donors to discontinue all financial aid to the Palestinian Authority, apart for "humanitarian assistance provided to the Palestinian population".
President Abbas said the world should "not punish the Palestinian people for their democratic choice".