Falk said the Geneva Convention required forces at war to be able to distinguish between military targets and civilians.
If that is not possible, then "launching the attacks is inherently unlawful".
Israel launched its offensive on the Hamas-run Gaza Strip in December saying it aimed to stop rocket fire by Hamas into southern Israel.
A ceasefire was declared on January 18 after the offensive left about 1,400 Palestinians dead, many of them women and children.
Three Israeli civilians and 10 soldiers were killed during the offensive.
Blockade 'a crime'
Falk said that the Gaza border blockade also was not legally justified and may represent a "crime against peace", a principle established at the Nuremberg trials of Nazi war criminals.
Sealing the border, denying people the right to flee the war zone as refugees, may also be a crime against humanity, his report said.
He said Israel's violations included alleged "targeting of schools, mosques and ambulances" during the offensive, and its use of weapons including white phosphorus.
He also condemned the firing of rockets at civilian targets in southern Israel by Hamas.
Falk called for an independent experts group to investigate possible war crimes committed by both the Israeli military and Hamas.
He recommended witness testimonies as well as explanations from Israeli and Palestinian military commanders.
Falk gave the same death toll from Israel's offensive in December and January - 1,434 Palestinians, 960 of those civilians - as the Palestinian Human Rights Centre.
Israel disputes the figures and accuses Hamas fighters in Gaza of using civilians as human shields.
Falk said Israel's allegation should be investigated.
Daniel Seaman, a spokesman for the Israeli government, rejected Falk's assertions, saying that his report contained no truth or legitimacy.
"The soldiers, questioned by our military authorities, are saying these [in the report] are not first-person eyewitness accounts ... these are stories they heard second hand," Seaman said.
He said every military in the world "at times makes mistakes".
|Israel said its offensive was to halt Hamas rocket fire into southern Israel [EPA]
But "if we find our soldiers violated the code of conduct [in war], they will be dealt with, with the utmost severity of our laws", Seaman said.
"We do not need a Richard Falk, who is notorious for his anti-Israeli position, to tell us how to conduct ourselves."
Falk said the UN Security Council might set up an ad hoc tribunal to establish accountability for war crimes in Gaza, noting Israel has not signed the Rome statutes establishing the International Criminal Court.
He was refused entry into Israel two weeks before the offensive started, preventing him from a planned mission to Gaza. In the report, he said the refusal had set an "unfortunate precedent" for treatment of a special rapporteur.
Speaking to Al Jazeera from Santa Barbara, California, Falk said he is not optimistic that his report will lead to concrete action.
"There is a lack of political will on the part of several major governments," he said.
"There has all along been a pervasive double standard with respect to the implementation of international criminal law.
"It has been applied to non-Western countries in the south and has exempted actors associated with Europe, North America and, generally, the north."
Rules of engagement
Falk's criticism came as reports surfaced in the Israeli media suggesting that Israeli forces killed Palestinian civilians under what may have been lax rules of engagement during the Gaza offensive.
Quoting Israeli soldiers who fought in the offensive, the Haaretz newspaper reported on Thursday that soldiers had ransacked and destroyed civilian property.
The soldiers' testimony, made at a course at Oranim Academic College in Tivon, runs counter to the Israeli army's claims that troops observed a high level of moral behaviour during the operation.
The testimonies include a description by an infantry squad leader in which he relates an incident where an Israeli sharpshooter shot a Palestinian mother and her two children, Haaretz reported.
If proved, the soldiers' testimonies could contribute to war crimes charges against Israel.
Al Jazeera's Hoda Abdel Hamid, reporting from Gaza, said that there was no doubt in the minds of Gazans that Israel committed war crimes during the assault.
"There is a certain level of satisfaction that these stories are coming out and that a body like the UN is saying the same things that they are saying," she said.