Hundreds of Palestinian civilians were killed in the 22-day conflict last winter
Israel has come under pressure from its allies to investigate UN allegations of possible war crimes by its army during its Gaza offensive last winter.
Britain's UN envoy urged Israel to hold "full, credible and impartial" investigations, echoing similar calls from his US and French counterparts.
A report by a UN mission led by Richard Goldstone accused both Israel and Palestinian militants of war crimes.
The UN Human Rights Council in Geneva is discussing the report again.
The findings were originally presented by Mr Goldstone, a veteran South African judge and war crimes prosecutor, to the Council two weeks ago, but it decided to defer its response until March.
However it reconsidered because of anger among Palestinians that allegations in the report were being ignored.
Israel has rejected the Goldstone report as biased and favouring terrorism.
"We note that the Israeli Defence Force has already conducted and is continuing to conduct a number of investigations," said John Sawers, the British Ambassador to the UN.
"However, concerns remain... We urge the Israeli government to carry out full, credible and impartial investigations into the allegations," he added.
French Ambassador Gerard Araud urged both sides to initiate "independent inquiries in line with international standards."
The deputy US Ambassador, Alejandro Wolff, expressed serious concerns about the report - citing an "unbalanced focus on Israel" - but he repeated the US view that Israel should look into it.
"We take the allegations in the report seriously," he said. "Israel has the institutions and the ability to carry out serious investigations of these allegations and we encourage it to do so."
The UN Secretary General Ban Ki-moon has urged "credible" investigations by both sides into the conduct of the Gaza conflict "without delay".
The Goldstone report accuses Israel of using disproportionate force and deliberately harming civilians during the 22-day conflict which began on 27 December 2008.
Palestinian Hamas militants are accused of indiscriminate rocket fire at Israeli civilians.
The report urges the Security Council to refer allegations to the International Criminal Court if either side fails to investigate and prosecute suspects.
Israel has rejected the evidence, saying it has already investigated its troops' conduct, clearing most of the subjects of wrongdoing. Hamas has also denied committing war crimes.
"For those of us who seek to resume the peace process in the Middle East, debating the Goldstone in the Security Council is but a tale full of sound and fury, signifying nothing," said Israel's envoy to the UN, Gabriela Shalev.
"If Israel is asked to take further risks for peace, the international community must recognise our right to self-defence," she added.
Israeli military action destroyed thousands of homes, hundreds of factories and 80 official buildings in Gaza.
Palestinians and human rights groups say more than 1,400 people were killed in the violence between 27 December 2008 and 16 January 2009, more than half of them civilians.
Israel puts the number of deaths at 1,166 - fewer than 300 of them civilians. Three Israeli civilians and 10 Israeli soldiers were also killed.