Palestinian Prime Minister Ahmed Qurei has announced his resignation, saying Hamas must form the next government following the parliamentary elections.
It comes as the militant Islamic group appeared to be heading for a shock win.
With counting still under way, officials from the ruling Fatah party said Hamas had won a majority. Official results are due at 1900 (1700 GMT).
Israel, the US and the EU consider Hamas a terrorist group and have said they do not want to deal with it.
"I am going to present my resignation to President Abu Mazen [Mahmoud Abbas] and Hamas should form the [new] government," Mr Qurei told journalists, according to AFP news agency.
Recognising Israel is not on the agenda
In pictures: Poll shock
Hours before official results were due to be released, Fatah officials privately admitted that Hamas had won.
Hamas claimed it had won at least 70 seats in the 132-member parliament.
The BBC's Jon Leyne in Jerusalem says there is no doubt that the Hamas showing has transformed the Palestinian political arena.
For decades, Fatah - the party founded by the late Yasser Arafat - has totally dominated electoral politics, but that time is over, he says.
Hamas is also now a major power and it will enter parliament still committed to its armed confrontation with Israel, our correspondent adds.
With victory looming, senior Hamas official Mushir al-Masri said the group wanted to work with Fatah in a "political partnership".
But he said Hamas would not hold peace talks with Israel.
"Negotiations with Israel is not on our agenda," he said.
"Recognising Israel is not on the agenda either now."
Speaking before Hamas claimed victory, acting Israeli Prime Minister Ehud Olmert said Israel could not deal with a Palestinian Authority which included Hamas.
"Israel can't accept a situation in which Hamas, in its present form as a terror group calling for the destruction of Israel, will be part of the Palestinian Authority without disarming," Mr Olmert's office reported him as saying.
"I won't hold negotiations with a government that does not stick to its most basic obligation of fighting terror."
The European Union - the biggest provider of aid to the Palestinian Authority - said it would work with any peaceful Palestinian government.
"We are happy to work with any government if that government is prepared to work by peaceful means," said European External Relations Commissioner Benita Ferrero-Waldner.
"Allah matlamat kami, Rasul pimpinan kami, Al-Quran perundangan kami, jihad jalan kami, syahid cita-cita kami" adiemad
NADIE SAKURA E-SHOP
1. Air Market
2. Jualan Busana Muslimah, Bahan-bahan ilmiah dll.
3. Ruangan Iklan Untuk Disewa
4. Artikel2 Menarik Dan Berita2 Terkini
5. Radio Online Dll