The "continued pattern of settlement expansion in East Jerusalem combined with the forcible eviction of long-residing Palestinians are creating an intolerable situation" in the part of the city previously controlled by Jordan, he said.
This situation "can only be described in its cumulative impact as a form of ethnic cleansing," Falk declared.
Israel declines to deal with Falk or even allow him into the country, accusing him of bias against the Jewish state.
In a linked discussion on Israeli policies towards lands it seized in the 1967 Middle East War, Israeli and Palestinian delegates clashed over the recent murders of members of a Jewish settler family on the West Bank.
Israel's ambassador Aharon Leshno Yaar called on Palestinian leaders to condemn the March 11 murders
of three children, including a baby, and their parents "without caveats or hedging" in Arabic to their own people.
Almost as shocking as the killings, "in the days following the massacre many Palestinians took to the streets celebrating the deaths of this family," Leshno Yaar said.
But Palestinian envoy Ibrahim Kraishi said the killings had already been condemned by the Palestinian Authority as "an act of terrorism" that was not part of his people's culture. "Rather, it is the culture of the occupying power," he added.
In his speech, Falk said he would like the Human Rights Council to ask the International Court of Justice to look at Israeli behaviour in the occupied territories.
This should focus on whether the prolonged occupation of the West Bank and East Jerusalem had elements of "colonialism, apartheid and ethnic cleansing inconsistent with international humanitarian law," the investigator declared.