Not satisfied with the presence of two foreign observers in Israelis internal inquiry, UN chief Ban-Ki moon is pushing for an international probe into the May 31 raid on a Gaza-bound aid ship that killed nine activists.
Israel set up a government-appointed commission called the Independent Public Commission, which includes two foreigners - Lord David Trimble, a Nobel Peace laureate from Northern Ireland, and Brig Gen Ken Watkin, former judge advocate general of the Canadian Forces.
"I know that there are going to be two international observers. But what I have heard from most of the countries is that it is not sufficient enough to have international credibility," Ban said.
Ban has also proposed an international panel under the aegis of a third party, in which both Turkey and Israel would actively participate.
Ban's proposal would include a panel of four members with one representative each from Israel and Turkey, headed by Geoffrey Palmer, a former New Zealand prime minister.
Turkey has accepted the proposal but Ban says he is still trying to convince Israel that the two panels could exist together.
"I've been telling them that my proposal is not incompatible with Israel's national investigation," Ban said.
Shortly after the raid, the UN Security Council had issued a presidential statement condemning Israel's interception of the aid convoy and calling for a "prompt, impartial, credible and transparent investigation".
Since then, many nations have supported an international investigation into the incident, with Turkey whose nationals died in the incident, being the most vocal.
But the US has been more muted in its criticism of its key ally and backed a domestic inquiry.
"The Security Council called for a prompt, impartial, credible and transparent investigation conforming to international standards," Ban said.
Claude Heller, the President of the Security Council and Mexico's envoy to the UN, noted last week that "for several members of the Security Council the Israeli commission is not enough".
While acknowledging Israel's recent decision to allow more goods into Gaza, Ban called for a "fundamental change" in the policies for Gaza.
"Much more is required to really meet the needs of the people," he said.