Speaking to students at Abu Dis' Al-Quds University on Monday, Fayyad said "I am proud to be talking to you at a university located in the heart of Jerusalem."
He then criticized the "Judaization of Jerusalem and the "isolation" of east Jerusalem's Arab population.
"A Palestinian state will be established in two years' time," the Palestinian PM told the students, adding that the US-backed Road Map for peace and the Arab peace initiative were the basis for any political process.
Fayyad, a technocrat with no significant political base of his own, heads a newly aligned cabinet with more ministers from the dominant Fatah faction of President Mahmoud Abbas, whose Islamist Hamas rivals refuse to recognize the premier.
"I call on all our people to unite around the project of establishing a state and to strengthen its institutions ... so that the Palestinian state becomes, by the end of next year or within two years at most, a reality," he said in his speech.
Fayyad also called for reconciliation between the various Palestinian factions, and said "the international community supports the Palestinians' positions."
The Palestinian PM also demanded a cessation of Israeli settlement building and called for lifting the blockade on the Gaza Strip.
Hamas spokesman Fawzi Barhoum said that Fayyad "has no right to speak about national unity".
Keen to prove their law-and-order credentials as part of efforts to revive peace talks with Israel, Abbas and Fayyad have been mounting increasingly bloody West Bank crackdowns on Hamas.
"He (Fayyad) creates the greatest danger for Palestinians by believing in the ongoing security coordination with the Zionist enemy," Barhoum said.
Reuters contributed to the report