The Quartet - which comprises the US, the UN, Russia and the EU - announced what it called a "temporary international mechanism" on Tuesday to resume aid payments to the Palestinians, but without dealing directly with Hamas.
The EU external relations commissioner, Benita Ferrero-Waldner, said details of the proposal should be fleshed out in the coming weeks.
The Middle East Quartet wants
Hamas to recognise Israel
The Palestinian Authority has been unable to pay employees for two months since the US and EU froze aid payments in protest over Hamas's unwillingness to change its founding principles.
The Quartet reiterated demands after its meeting in New York that Hamas should renounce the use of violence, recognise Israel and respect previous international accords.
It also called on Israel to stop settlement expansion.
Ismail Haniya, the Palestinian prime minister and senior Hamas member, said those conditions "aim to push the Palestinian government to make concessions that harm [Palestinian] rights and red lines and give the [Israeli] occupation legitimacy".
Hamas has said it would regnonise Israel only if it withdrew from the territories it seized in 1967 - including east Jerusalem - freed all Palestinian prisoners and allowed refugees to return to their homes, most of which are now in Israel.
An ally of Mahmoud Abbas, the Palestinian president, said the authority welcomed the Quartet's demand for a negotiated settlement with Israel, in line with its so-called road map.
Saeb Erekat, the chief Palestinian negotiator, said: "We welcome the Quartet's insistence on the road map and on a negotiated settlement between the two parties to resolve issues such as the borders and their appeal for the Israeli government to stop the settlements."
Erekat, who works with Abbas rather than the Hamas government, also said he hoped that the new funding mechanism would allow the rapid resumption of aid.
"We hope that the donor countries will rapidly resume aid so that a humanitarian catastrophe can be avoided," said Erekat.
Israel, meanwhile, said it accepted the resumption of aid to the Palestinians though it had pushed hard and successfully for financial assistance to the Palestinians to be severed after the Hamas-led administration took power in March.
"As far as we are concerned, the Quartet's decision to give further humanitarian support to the Palestinian Authority, bypassing the Hamas government, is definitely OK"
Tzipi Livni, the Israeli foreign minister, said: "As far as we are concerned, the Quartet's decision to give further humanitarian support to the Palestinian Authority, bypassing the Hamas government, is definitely OK."
Russia, the European Union and the United Nations had all put pressure on the United States, which has taken the toughest stand against Hamas, to agree to ease the boycott.
The powers agreed that aid payments would be resumed for a three-month trial period, through a "transparent" mechanism that has yet to be worked out.
It is expected that salaries to the Palestinian Authority's 165,000 employees, unpaid since March, will be paid. The monthly wage bill is about $150 million.
Javier Solana, the EU foreign policy chief, said after the initiative was announced that "If you need a hospital to be run, and someone has to be paid, he will be paid."
Israel is withholding about $55 million a month in tax receipts that it collects on the Palestinians' behalf, and has frequently closed the main commercial goods terminal on its border with Gaza, citing security concerns.
But there was no indication that it would alter its policies.