Falk also called for an investigation into Israel's attack on Gaza, in which more than 1,300 Palestinians were killed and homes destroyed.
Israel said it carried out the assault to stop Palestinian rocket attacks on southern Israel.
Falk's comments formed part of a much longer report from nine UN investigators including specialists on the right to health, food, adequate housing and education, as well as on summary executions and violence against women.
"We've found the rapporteur's views to be anything but fair. We find them to be biased. We've made that very clear"
Robert Wood, US state department spokesman
Radhika Coomaraswamy, the UN secretary-general's Special Representative for Children and Armed Conflict, accused Israeli forces of using a child as a human shield in one incident.
Soldiers forced an 11-year-old boy to walk in front of them for several hours as they moved through the town of Tal al-Hawa on January 15, even after they had been shot at, her report said.
Aharon Leshno Yar, Israel's ambassador to the UN rights council, condemned the report, saying it "wilfully ignores and downplays the terrorist and other threats we face", and the alleged use by Palestinian fighters of human shields.
The US accused Falk of being biased.
"We've found the rapporteur's views to be anything but fair. We find them to be biased. We've made that very clear," Robert Wood, a US state department spokesman, told a media briefing on Monday.
Falk called for the probe to assess if the Israeli forces could differentiate between civilian and military targets in Gaza.
"If it is not possible to do so, then launching the attacks is inherently unlawful, and would seem to constitute a war crime of the greatest magnitude under international law," Falk said in the report.
"On the basis of the preliminary evidence available, there is reason to reach this conclusion," he added, saying that attacks occurred in densely populated areas.
Falk, who has been critical of Israel in the past, was expelled from Israel during an attempt to visit Gaza in December, after he said Israel's policies on the territory amounted to a crime against humanity.