Western countries are concerned by Hamas' refusal to renounce violence and recognize Israeli statehood.
Factional fighting between Fatah and Hamas claimed more than 90 Palestinian lives between December and February.
In the past four days, Hamas has fired over 422 rockets into Israel.
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Today, some of the world's leading diplomats are deciding what to do about Hamas.
Mr. MARK REGEV (Israeli Government Spokesman): Unequivocally there are no direct or indirect talks with Hamas.
Mr. REGEV: Hamas would like a time-out, a time to rest and regroup and rearm.
Our correspondent says it remains to be seen if Hamas will enforce the legislation.
Their movement is controlled by both Israel's blockade of Gaza and by the Hamas government.
"They are committed to our destruction, " Former Prime Minister Benjamin Netanyahu said of Hamas.
Of the 375 Palestinians killed, most were Hamas militants, Palestinian medical sources said Tuesday.
Earlier in the day, Israeli forces took "tens of Hamas militants" into custody, the military said.
Abbas' Fatah group dominated Palestinian politics for decades until last year, when Hamas won legislative elections.
CNN: Palestinian fighting 'will burn all of us,' official says
Critics of Hamas accuse it of increasingly imposing laws that reflect a conservative interpretation of Islam.
The call comes after the reconciliation between Hamas and Fatah brokered last week by Egypt.
President Bush, for his part, is openly disgusted with Hamas and its US-based supporters.
The United States and Israel later refused to recognize the legitimacy of the Hamas win.
The Quartet wants Hamas to recognise Israel, renounce violence and honour existing Palestinian agreements with Israel.
Their policy began under American pressure soon after Hamas won a Palestinian general election in 2006.
That will give Hamas a right of veto over big decisions, including negotiations with Israel.
By the end of the official truce on December 19th, Hamas's harder-liners again held sway.
His Fatah movement, based in the West Bank, is deeply split from Hamas, which governs Gaza.
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Ahmed Said Khalil al-Jabari, head of Hamas' military wing, was killed in the initial air strike.
Mr Abbas made Mr Dahlan, Hamas's nemesis, secretary of a new national security council.
The Quartet says it will not engage with Hamas unless, among other things, it recognises Israel.
For instance, they always say that the Fatah movement wants Hamas to recognize Israel.
No country on earth will volunteer to fight Hamas and its jihadist allies in Gaza.
The ministry said the report does not mention Hamas' "deliberate use" of civilians as human shields.
But the poll in the Gaza strip, where Hamas is strong, was put off.
None have publicly recognized that Israel has a duty to its citizens to defeat Hamas.
Indeed, he said that Fatah agreed to add annexes to the agreement reflecting Hamas's positions.
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