Also known as Abu Ala, he is now charged with reviving the American-backed "road map" to peace after the departure of ex-premier Mahmud Abbas.
As one of the Palestinian Liberation Organisation’s most senior leaders, Quraya's supporters say he has the trust and respect of all sides in the conflict.
But his detractors say he is too close to the Israelis, and the imminent collapse of the process he helped to initiate hardly bodes well.
Quraya, 65, was born in Abu Dis, Jerusalem, in 1937.
He became a banker by trade and joined Yasir Arafat's Fatah organisation in the 1960s.
However, he did not come to prominence within the PLO until a decade later when he took over its economic and production arms in Lebanon.
When the PLO was forced out of Lebanon by the Israelis in 1982, Quraya followed Arafat into exile in Tunisia.
Over the years he gradually gained more influence within the organisation until he was elected a member of the Fatah central committee in 1989.
But his main claim to fame is as one of the architects of the Oslo peace accords with Israel in 1993.
These led to limited Palestinian autonomy in the West Bank and Gaza Strip and the return of senior PLO leaders from exile.
They were also meant to be the precursor to a permanent settlement between the two sides.
In 1996, Quraya was elected the Speaker of the Palestinian Legislative Council - a role which means he will succeed Yasir Arafat in the event of his death.
The Americans and Israelis have
refused to negotiate with Arafat
Abu Ala is said to be a man of great charisma which has won him friendships over the years with his Israeli counterparts.
In July 1999, he even accepted an invitation to visit Israel's parliament, the Knesset, where he met its speaker.
He is generally considered one of the few Palestinians who have credibility with Israel, but who can also count on the backing of Arafat.
But in the end, these close ties with the Jewish state may be his undoing in the eyes of many Palestinians.
Despite his exalted status in the PLO he has no real power base within the organisation or among the masses.
Another potential handicap is his frail health after several heart attacks.
Israel's Shimon Peres even rode by his side in the ambulance that took him to an Israeli hospital after one such seizure.
An emotional Quraya later thanked Peres and said he had saved his life.
Analysts say Abu Ala has accepted a poisoned chalice by taking the prime minister’s position.
Whether his health, credibility and negoitiating skills will be up to the job remains to be seen.
But one thing is sure - if he does no better than Mahmud Abbas it could sound the death knell for his life's work.