The commission released its report on the 50-day conflict on Monday.
"The extent of the devastation and human suffering in Gaza was unprecedented and will impact generations to come," the chair of the commission, New York judge Mary McGowan Davis, said in a statement.
The report decried the "huge firepower" used in Gaza, with Israel launching more than 6,000 airstrikes and firing 50,000 artillery shells during the 50-day operation.
"The commission is concerned that impunity prevails across the board for violations of international humanitarian law and international human rights law allegedly committed by Israeli forces," the report said.
"Israel must break with its recent lamentable track record in holding wrongdoers accountable, not only as a means to secure justice for victims but also to ensure the necessary guarantees for non-repetition.
"With regard to Palestinian armed groups, the commission has serious concerns with regard to the inherently indiscriminate nature of most of the projectiles directed towards Israel by these groups and to the targeting of civilians, which violate international humanitarian law and may amount to a war crime."
The commission, composed of chair Davis and Senegalese lawyer and human rights expert Doudou Diene, was launched a year ago at the request of the Palestinians.
"We must remember that the victims are not just numbers ... they are individual people," Davis said as she released the report in Geneva.
Al Jazeera's Imtiaz Tyab, reporting from West Jerusalem, said that the report called on both sides to show political leadership and to cooperate with International Criminal Court investigators.
Tyab said Israel immediately labelled the UN commission's report as "morally flawed" and "grossly biased".
A ceasefire last August ended 50 days of fighting between Gaza fighters and Israel.
The UN has previously said that most of the 2,139 Palestinians killed in the conflict were civilians, while 66 Israeli soldiers, six Israeli civilians and one Thai national also died.
Israeli air strikes and shelling hammered the densely populated enclave dominated by the Hamas movement, causing widespread destruction of homes and schools. Gaza fighters fired thousands of rockets and mortar bombs into Israel.
Pre-empting the findings of the UN report, Israel defended its conduct in the 2014 Gaza war as both "lawful" and "legitimate" in a detailed inter-ministerial report released earlier this month.
"Hamas' strategy was to deliberately draw the hostilities into the urban terrain, and to use built-up areas and the presence of the civilian population for tactical advantage and political gain," the Israeli 242-page document said.