Israeli forces shelled a house in the Gaza Strip which they had moved around 110 Palestinians into 24 hours earlier, the UN quotes witnesses as saying.
The UN Office for the Coordination of Humanitarian Affairs (OCHA) called it "one of the gravest incidents" since the beginning of the offensive.
The shelling at Zeitoun, a south-east suburb of Gaza City, on 5 January killed some 30 people, the report said.
Israel said the allegations were being investigated.
"According to several testimonies, on 4 January Israeli foot soldiers evacuated approximately 110 Palestinians into a single-residence house in Zeitoun (half of whom were children) warning them to stay indoors," the OCHA report said.
"Twenty-four hours later, Israeli forces shelled the home repeatedly, killing approximately 30."
The UN said those who survived and were able walked 2km to the main north-south road to be transported to hospital in civilian vehicles.
"Three children, the youngest of whom was five months old, died upon arrival at the hospital," the report said.
'No safe haven'
Allegra Pacheco, of OCHA in Jerusalem, said they were not accusing the Israelis of a deliberate act, but said the incident needed to be investigated.
She also said they were concerned at claims by the International Committee of the Red Cross (ICRC) that ambulances were only allowed access to the neighbourhood on Thursday - four days after the alleged incident.
The ICRC on Thursday accused Israel of failing to fulfil its duty to help wounded civilians in Gaza.
"In Gaza, there is a severe protection of civilians crisis. There is no safe haven, no safe space, for all the civilians, particularly children," Ms Pacheco told the BBC.
"Since the ground operation, the number of children killed has risen by 250%."
An estimated 770 Palestinians and 14 Israelis have died in nearly two weeks of Israel's air and ground offensive against the Palestinian militant group Hamas.
The UN Security Council has called for an immediate ceasefire and the withdrawal of Israeli troops from Gaza.
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