"The stabbing attack in the Old City exposes the illusion that it's possible to deprive an entire people of rights and sovereignty without the desperation turning into frightful hatred and violence".
Israeli police forces opened fire on the assailant and he was "likely dead", the spokesperson said.
The Walla! news site reported that members of the left-wing Meretz party, and the Peace Now and Breaking the Silence organizations were also in attendance.
Saturday's march is the first in a series of planned action marking the 50 anniversary of the Israeli occupation.
A Palestinian attacker from the West Bank who stabbed and wounded three Israelis was shot dead by police near the Old City's Damascus Gate.
Almost 400,000 Jewish settlers are now living in the West Bank along with 2.8 million Palestinians.
Netanyahu announced on Thursday to his ministers that Israel would self-impose restrictions on settlement building that is subject to constant condemnation by Palestinians and the worldwide community, considering it completely illegal, Efe news reported.
Assistant to the President and Special Representative for International Negotiations Jason Greenblatt meets Prime Minister Benjamin Netanyahu at the Prime Minister's Office in Jerusalem, Monday, March 13, 2017.
Israel's so-called security cabinet on Thursday unanimously voted in favor of the construction of the first new West Bank settlement in 20 years.
Meanwhile, Israel's decision to build a new community for the former Amona residents was harshly condemned by United Nations Secretary-General Antonio Guterres and European Union Foreign Policy Chief Federica Mogherini.
It further called on Israel to immediately and completely cease all settlement activities on the occupied territories.
The two-state solution, that Israel claims to agree to and for which an entire "peace talks" industry has been in motion for decades now, is conditional on full Israeli withdrawal from the West Bank, including East Jerusalem.