"He told President Yasir Arafat and the Legislative Council that he accepted, in principle, the position of prime minister," said information ministry spokesman Dr Ahmad Subh.
Quraya himself was not immediately available for comment.
The timing of Quraya's decision to accept the post - albeit informally - is somewhat unexpected and apears to soften his initial stance.
He had previously said he would only take up the premiership if he were assured of necessary international support and if Israel showed a willingness to change its behaviour towards the Palestinians.
“I don't want to see assassinations and demolitions of houses. I want to see a real ceasefire. These are my conditions,” Quraya told reporters earlier in the day.
But Quraya's acceptance has so far not been welcomed by Israel, which sees him as too close to the Palestinian president. Israeli Foreign Minister Silvan Shalom reportedly dismissed news of Quraya's nomination to the post as irrelevant only hours before his acceptance was announced.
Past and present: Mahmud Abbas
(L) resigned his post on Saturday
"We were not expecting a warm welcome from their side," Subh told Aljazeera.net.
"(Israeli Prime Minister) Ariel Sharon is seeking to avoid any political talks and any implementation of Israel's commitments to the peace plan."
"We're waiting for pressure from Washington to make them carry out their obligations," he said, referring to the so-called road map, the peace plan drafted by the United States and sponsored by the "quartet" of the US, the United Nations, the European Union and Russia.
Quraya has been conferring with representatives of the quartet in the past 24 hours, asking them to back his future cabinet and help revive stalled peace negotiations.
The United States, Israel's chief ally, has so far been cautious about Qaraya's likely appointment. But the three other members of the quartet have expressed their support for the incoming prime minister, Subh said.
EU foreign policy chief, Javier Solana, has described the Palestinian official as "a man of peace" whom the EU would do all it could to help.
Quraya, who is the current speaker in the Palestinian parliament, was asked by Palestinian leader Yasir Arafat on Sunday to succeed Prime Minister Mahmud Abbas.
Abbas resigned on Saturday, saying he had insufficient support domestically and internationally, and had been undermined by Israeli actions.