Russia and the UN have said they will use the Berlin meeting to push for the unity government to be recognised.
"I count on the Quartet speaking out in support of the agreement to form a new Palestinian government," Sergei Lavrov, the Russian foreign minister, said in an interview with Russian newspaper
Rossiyskaya Gazeta.
Russia has long standing objections to the Quartet's list of conditions and wants to establish contact with Hamas and lift the aid embargo.
'Encouraged'
Ban Ki-moon, the UN secretary-general, said in Berlin ahead of the talks that he was "encouraged" by the power-sharing deal that was agreed in Mecca on February 8.
The Europeans are also thought to view the agreement as the best chance to avoid civil war in the Palestinian territories.
An EU official told the Reuters news agency that foreign ministers from the 27-member bloc are inclined to see the Mecca agreement as "a glass half full, rather than half empty".
The US has said that it will wait until the new government is formed and its political programme announced, a process that could take up to five weeks, before it takes a formal decision on whether to reject the agreement.
"We don't know how it's going to be put into practice," Condoleezza Rice, the US secretary of state, said after a recent meeting with Abbas. "There's very sparse data at this point about this government."
Rice is expected to call on the Quartet to play a bigger role in trying to revive Israeli-Palestinian peace moves and keep up pressure on Hamas.
Jerusalem summit
She will also report on a summit she hosted in Jerusalem on Monday between Abbas and Ehud Olmert, the Israeli prime minister, which apparently made little progress.
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A senior US official told AFP that Washington would be urging the EU to take stronger measures to assist Abbas and improve his position, potentially sidelining the ruling Hamas party.
The meeting is expected to agree to a European Union proposal to expand a temporary financial mechanism which has permitted the delivery of $160m in humanitarian aid to the Palestinians since July last year.
Under the proposal, EU funds could also be used to build up Palestinian institutions controlled by the Abbas presidency.
Hamas said it hoped that Washington and the rest of the Quartet would soften their position, while Arab nations such as Egypt and Saudi Arabia, also believe the new government should be given a chance.