Qorei told journalists: "I am going to present my resignation to President Abu Mazen (Mahmoud Abbas) and Hamas should form the government."
Although results have yet to be confirmed by the official Palestinian election authority, officials from Abbas' ruling Fatah faction of President have confirmed claims from Hamas to have won a majority of seats.
That would put the party in position to shape a new Palestinian government - a situation that could dim prospects for restarting peace talks with Israel.
Palestinian leader Mahmoud Abbas has said he would step down if he could no longer pursue his peace agenda with Israel.
Hamas leaders in both the West Bank and Gaza Strip have indicated that the movement may have won as many as 70 seats out of the 132 contested seats, making up the Palestinian legislative council.
Hamas' leader in Gaza, Ismael Haniyah, said he had "solid information" indicating the movement won more than 50% of the overall vote.
With results still being collated, that projection seems to be ringing true.
In Hebron, Hamas won all the nine contested seats at the district level, with Sheikh Nayef Rajoub, coming top.
A Hamas win will further cloud
peace prospects with Israel
All Fatah and Fatah-affiliated candidates are reported to have failed to win seats, these include former Palestinian Authority leaders such as Jebril Rajoub (Nayef's brother), as well as former ministers Nabil Amr, Jamal Shubaki and Rafik Natsheh.
Moreover, a myriad of independent candidates have been unsuccessful in their bid to win a seat.
Conversely, Hamas performed strongly in other districts and other areas once considered solid ‘Fatah territory’, such as Nablus, Salfit, Tubas and Tulkarm.
In Ramallah, the PA capital and Fatah's stronghold, Hamas reportedly won all the four contested seats.
There are also unconfirmed reports that Hamas won all or most of the contested seats in East Jerusalem.
Likewise, in Gaza Hamas seems to have defeated Fatah in most districts.
"It is obvious that we are witnessing the beginning of a new era"
Talal Ukal, political analyst
Meanwhile, Fatah officials have begun to acknowledge that the political landscape has changed.
Fatah West Bank leader Hussein al Sheikh said during an interview with Israeli radio that Fatah was slowly coming to terms with Hamas's victory.
He said Fatah would have to have "a lot of soul searching with itself"
He also stressed that Fatah supporters ought to respect the will of the people and refrain from lawless activities.
The PA security chief blamed Israel for "Hamas' victory," saying the collapse of the peace process, rampant corruption and lawlessness have convinced the bulk of the Palestinian people that voting for Fatah is futile.
While Fatah’s defeat was a comparatively close one, leftist, liberal parties and independent candidates have apparently suffered a devastating electoral blow.
According to the latest results, all other lists, including Mustafa al Barghouthi's Independent Palestine, will receive only a handful of seats.
Barghouthi said during televised interview on Wednesday night that he was sure his movement would win at least 15% of the total vote.
Similarly, the Third Way, a liberal list led by former finance minister Salam Fayyad seems to have won no more than three seats.
Fatah supporters initially took
to the streets in celebration
Talal Ukal, a Palestinian commentator and political analyst, described the election as a watershed.
"It is obvious that we are witnessing the beginning of a new era and we all must come to terms and adapt to the new reality," he said on Thursday.
In Ram Allah, Hamas and Fatah activists clashed at the Palestinian parliament on Thursday after Hamas won the elections, witnesses said.
A Reuters witness said the trouble started after Hamas members hoisted a green Hamas flag at the entrance to the building, and Fatah supporters tried to tear it down.
Shooting briefly erupted during the melee, witnesses said. At least two people were injured but it was unclear whether they were wounded by gunfire. Police said there were no serious casualties.
Several windows were broken at the parliament building by stone throwers.
Palestinian security forces rushed to the scene to try to disperse the rivals.