His announcement has ended days of political suspense and high drama which has plunged the Palestinian Authority into chaos after the resignation of Mahmud Abbas.
Quraya, accepting his nomination on Wednesday, said he would also form an emergency government.
"The president asked and urged me strongly to accept to form a government. I agreed and I have got to face this crisis, to face this problem," the veteran Palestinian leader said.
"I will take the risk. I will take the responsibility. I will go forward," Quraya told reporters.
"I hope I will be able to form an emergency government, a six, seven or eight-person government," he added.
Quraya takes over the job amid spiraling violence and heightened tensions between the Palestinians and Israelis, even as the US-backed peace ''road map'' for the region lies in virtual tatters.
Mahmud Abbas resigned last Saturday after barely 100 days in office, having fallen out with Arafat over the control of Palestinian security and police forces.
"The president asked and urged me strongly to accept to form a government. I agreed and I have got to face this crisis, to face this problem"
Arafat named Quraya as Abbas's successor on Sunday.
Speaking to reporters, Quraya also condemned the Israeli air strike in Gaza, that killed three people and injured Hamas leader Mahmud al-Zahhar on Wednesday.
"What happened today in Gaza is very dangerous and is not acceptable," the Prime Minister-designate said .
He was quick to condemn Tuesday's bomb explosions in Tel Aviv and Jerusalem that left 15 persons dead and scores wounded.
"What happened from the Palestinians is unacceptable and is dangerous," he said.
"We are passing in a very dangerous historical moment. Each side should hold its responsibility carefully. We shoud put emotion aside and think seriously about the interests of both our people, Quraya said.
Quraya had earlier said the Israelis must resume peace talks with Palestinians in order to bring an end to the bloodshed.