A Hamas win would potentially disrupt the stalled Middle East peace process.
"I am going to present my resignation to president Abu Mazen (Mahmoud Abbas) and Hamas should form the government," Mr Qorei told journalists.
His comments came shortly after officials in the ruling Fatah faction conceded they had lost, and a source in the central elections commission said Hamas was ahead in the vote count.
"Hamas has beaten Fatah in the elections," said one senior Fatah official, speaking on condition of anonymity, according to an AFP report.
A separate candidate and senior member of the Fatah campaign agreed that Hamas had won.
"They have won more seats than us in the legislative council," he said.
Exit polls earlier indicated that Fatah had beaten Hamas by a slim margin, although had lost its majority.
The official result will not be announced until 7pm local time (4am AEDT), however Hamas has said it is confident of gaining an absolute majority.
A Hamas victory in the first Palestinian election in a decade would likely have a major impact on the Middle East peace process.
Both Israel and the United States have said they would not deal with a Palestinian government that includes Hamas.
Hamas claims victory
Hamas spokesman Sami Abu Zuhri insisted his movement has won at least 75 seats.
"Hamas has registered a considerable victory. Countries in the region and the international community must respect our people's choice, which is the result of democracy," said the group's chief candidate, Ismail Haniya.
However he was cagey on the subject of the movement's potential participation in the Palestinian government, talking only of "political partnership".
"In the light of these first results, we will consult president Abu Mazen (Abbas) and the Fatah brothers on the type of political partnership," he said.
But Israeli acting Prime Minister Ehud Olmert said Hamas, with its history of dozens of suicide bombings in the past five years aimed against Israelis, would not gain the Jewish state's approval to become part of the Palestinian Authority.
"Israel cannot allow Hamas to become part of the Palestinian Authority in its current form," Olmert said.
And US President George W Bush said his country will continue to blacklist Hamas, saying a political party needs to advocate peace if it is to be viable.
The election commission puts voter turnout at 73 percent.
Observers from the United Nations, the European Union and other international organisations said the poll passed off peacefully.