The International Committee of the Red Cross also reminded both parties - Israel and the Islamist Hamas movement - to the week-old conflict of their obligation to comply with humanitarian law to minimize civilian casualties.
At least 57 Palestinian civilians, including 18 children, are confirmed as having been killed, according to UN monitors who say the death toll had doubled in the past 48 hours. Ten more people were killed overnight but it was unclear how many were civilians, UN rights spokesman Rupert Colville said.
"The High Commissioner therefore calls on Israel to scrupulously meet its legal obligations to distinguish at all times between civilians and combatants and take precautions and all possible measures to avoid the loss of civilian life and damage to civilian property," Colville told a news briefing.
Some 31 residences in Gaza and two buildings used by media have been hit by Israeli missiles so far, and hundreds of people have been injured, he said.
Dozens of schools and religious sites in Gaza are reported to have been damaged by Israel's aerial bombing campaign, which followed weeks of increasing Hamas rocket fire into Israel.
"As to whether these would be war crimes, that would depend very much on the circumstances of each individual episode as to whether there was a valid (military) target nearby or not, but that's a very complex issue," Colville said.
He said Navi Pillay, the UN High Commissioner for Human Rights and an ex-U.N. war crimes judge, felt it was necessary to ensure accountability for any violation of international law, including through independent investigations.
"Partners in Gaza tell UNICEF that children are increasingly showing signs of severe psycho-social distress. This includes an inability to sleep, being afraid to go out in public, clinging to parents, bed-wetting, nightmares and withdrawal," UNICEF spokeswoman Marixie Mercado told reporters in Geneva.Avoiding civilian casualties
Under international law, all sides are obliged to abide by three principles governing the rules of war. These include a need to distinguish between combatants and civilians and taking all possible precautions to avoid civilian casualties.
"The Israelis are saying that's what they are doing and yet there are a lot of civilian casualties taking place. So that needs further examination as to whether the principle of precaution is being properly followed," Colville said.
Proportionality means refraining from launching an attack when it is expected to cause excessive loss of civilian life in relation to the anticipated military advantage, he said.
Israel says it takes great care to avoid civilian casualties and accuses Hamas and other militant groups of deliberately putting Gaza's 1.7 million people in harm's way by placing rocket launchers among them.
Pillay also condemned "the continuing indiscriminate attacks and targeting of civilians in Israel by militants from Gaza" whose rockets have killed three Israeli civilians, injured others and damaged civilian property, Colville said.
UN Secretary-General Ban Ki-moon called on Tuesday for an immediate ceasefire in the Gaza Strip and US Secretary of State Hillary Clinton headed to the region with a message that escalation of the week-long conflict was in nobody's interest.
The ICRC said it was in regular contact with Israeli and Palestinian authorities, reminding them of their legal obligations "regarding means and methods of warfare".
But mounting casualty figures are making the situation difficult for Gaza's main hospitals and it is hard to maintain deliveries of medicines and medical materials, it said.
GENEVA (Reuters) -- The UN's human rights chief pressed Israel on Tuesday to avoid strikes on civilian structures in Gaza, and UNICEF said children in the enclave were showing signs of severe trauma after direct hits on dwellings that have killed dozens of civilians.