An Israeli official said the money would be turned over to Abbas by Friday.
"This is supposed to be spent according to Palestinian priorities. It is not for Israel to determine where it goes"
Samir Abu Aishah, Acting Hamas Finance Minister
The transfer, which will help to ease the serious cash-flow crisis suffered by the Palestinian Authority, was promised by Olmert when he met with Abbas on December 23.
But it will not be used for salaries of government workers, who have not been fully paid since Hamas took office.
Hamas angrily criticised the Israeli restrictions on the money, after Israeli officials said they needed assurances the money would not reach the movement.
Israel collects about $50 million in taxes from the Palestinians each month, which has contributed to a financial crisis for the Hamas-led Palestinian government.
Samir Abu Aishah of Hamas, the acting finance minister for Hamas, said that the government should decide how the money is spent.
"This is supposed to be spent according to Palestinian priorities. It is not for Israel to determine where it goes," he said.
"We have no problem if that money goes through the president's office, but it must be spent in the areas in which they are needed, according to our priorities."
Abbas has been pushing Hamas to join his party in a moderate coalition government, hoping to end the international boycott against the Palestinian government.
On Saturday, he is scheduled to travel to Syria for talks with Khaled Meshaal, the exiled Hamas leader, in hopes of working out a deal.