"I'm saying to the American administration, to President Bush to the Israelis and to the whole world, now is the period where we should be more serious," Qurei said.
"If we are determined to do it we can do it in a very short time."
He said there would be an election to replace Arafat by January 9, the BBC reported.
Arafat died after suffering multiple-organ failure, but the exact cause of his illness was not known Saturday.
A military funeral was held in the Egyptian capital Cairo and he was buried in the West Bank town of Ramallah near the battered compound where he was confined by Israeli forces for more than two-and-a-half years.