The money is the third in a series of payments provided by Qatar to help ease the grim economic and humanitarian situation in Gaza. The cash transfers, delivered through an Israeli crossing, have been controversial in Israel, where critics accuse the government of rewarding Hamas violence.
Prime Minister Benjamin Netanyahu blocked the latest transfer on Tuesday after a Palestinian sniper shot an Israeli soldier along the Gaza border, hitting him in the helmet and lightly wounding him. But the Israeli official said Thursday that security officials had now decided to allow the transfer. He spoke on condition of anonymity because he was not authorized to speak to the media.
Hamas is to use the money to pay thousands of civil servants who have not received full salaries in several years. As Israel was approving the payment, however, Hamas announced that it would not accept the money.
Khalil al-Hayya, a top Hamas official, said the group was protesting Israeli delays and "blackmail." Accusing Israel of violating understandings, he said Hamas has informed Qatari mediator Mohammed al-Emadi, who was in Gaza, of its decision.
He also vowed to step up a planned protest along the Israeli border on Friday. Hamas has staged regular protests along the border since last March to protest an Israeli blockade that has devastated Gaza's economy. Israel and Egypt imposed the blockade after Hamas, an Islamic militant group that seeks Israel's destruction, seized control of Gaza in 2007.
More than 185 Palestinians have been killed in the demonstrations, while an Israeli soldier was shot dead in July by a Gaza sniper. Israel accuses Hamas of using the large crowds as cover to carry out attacks.
Fares Akram in Gaza City, Gaza Strip, contributed reporting.