Jacques Chirac, the French president, proposed it on Friday before he met Mahmoud Abbas, his Palestinian counterpart in Paris.
Jerome Bonnafont, Chirac's spokesman, said France would raise the issue during talks on May 9 with the United Nations, the United States, the European Union and Russia - the four international players behind the stalled "road map" peace plan.
Ghazi Hamad, the Hamas administration spokesman, said salary payments "should be co-ordinated with the government", to prevent what he called "the creation of a second government".
Omar Abdelrazek, Hamas finance minister, said: "In principle we don't have a problem with that. But we have to talk about the details and preserve the rights of the ministry of finance to control and oversee all the financial procedures."
France and other European Union nations earlier this month cut off direct aid to the Palestinian government after Hamas's election victory. The European Union is the largest donor to the Palestinians, with aid totalling more than $600 million a year.
Because of international sanctions, the Hamas-led government has been unable to pay salaries to 165,000 Palestinian government employees.
France believes aid "must be maintained for humanitarian reasons, as well as for political reasons," Chirac said. "And it will push for this continuance [of aid] within the international community and notably within the European Union."
"The situation is very grave, complex and sensitive"
Abbas confirmed at a later news conference that the World Bank channel was among those discussed with Chirac to get aid to the Palestinian people.
"If we do not reach a solution, it will be catastrophic," he said. "The situation is very grave, complex and sensitive."
Chirac said humanitarian aid must be maintained and enlarged "in particularly through the agencies of the United Nations," his spokesman said. He said aid must channel through institutions independent of the Palestinian government.
The French leader also suggested that more aid could be placed under the authority of Abbas, a moderate, his spokesman said.
Chirac asked Hamas to respect the demand to renounce violence and recognise Israel's right to exist. The group has refused to temper its views.
Abbas, whose Fatah movement was defeated by Hamas in January's legislative elections, has worked to try to keep the West from shunning the Palestinians over the resistance group's anti-Israel ideology.