The statement said the investigation should be "prompt, impartial, credible and transparent".
It also condemned the "acts" which led to the deaths of at least 10 civilian activists during the operation.
The raid sparked strong international condemnation and calls for Israel to lift its three-year blockade of Gaza.
The UN statement was reached after hours of discussion as the council deliberated through the night.
In Turkey, Prime Minister Recep Tayyip Erdogan called Israel's raid a "bloody massacre" as he addressed parliament.
Egyptian President Hosni Mubarak has ordered the border crossing between Egypt and the Gaza Strip to be opened.
The Egyptian state news agency said it was to allow humanitarian aid through. It is not clear how long the crossing at Rafah will be kept open.
The UN statement was the result of a compromise between Turkey and the United States, with Turkey reluctant to water down its trenchant criticism of Israel while the United States, Israel's closest ally, wanted to temper the language used, says the BBC's UN correspondent Barbara Plett in New York.
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