The UN statement said Ban had told the panel "they should seek the fullest cooperation of the national authorities", a reference to Israel and Turkey.
Ban set up the inquiry last week into the May 31 raid at sea in which Israeli commandos killed nine Turkish pro-Palestinian activists after boarding their vessel, the Mavi Marmara, which was attempting to run Israel's naval blockade of the Gaza Strip.
At Tuesday's meeting the UN panel sought to head off any potential clash with Israel over the inquiry.
'No secret deal'
On Monday Ban denied the world body had struck a secret deal with Israel not to call Israeli soldiers to testify, saying there was "no such agreement behind the scenes".
Al Jazeera's Kristen Saloomey reporting from the UN said the credibility of the UN inquiry was already being questioned even before the panel's first meeting.
"Ban said that the panel itself will decide exactly how to proceed, how to go forward in cooperation with authorities from Israel and Turkey, and will focus on how to avoid such incidents in the future," said our correspondent.
"Israel will not cooperate with, and will not participate in, a panel that demands to investigate Israeli soldiers"
Mark Regev, Israeli government spokesman
"Israel apparently had a different opinion about what to expect from this panel however, and is calling into question as to how independent the investigation could be if it is going to rely only on local investigations."
The assault led to a sharp deterioration in Israeli-Turkish relations and forced Israel to ease the blockade of Gaza, which it says is to prevent Palestinian Hamas fighters from acquiring the military capability to attack Israel.
Israel, which has completed its own military investigation of the incident and started a civilian one, eventually agreed – at what diplomats said was the urging of the United States – to cooperate with the investigative panel set up by Ban.
In response to Ban's denial of a secret deal, Mark Regev, an Israeli government spokesman, said: "Israel will not cooperate with, and will not participate in, a panel that demands to investigate Israeli soldiers."
Regev did not say whether there had been a deal on the issue.
The UN said the panel's tasks will be to study the results of both Israeli and Turkish investigations of the flotilla raid, and to recommend ways to avoid similar confrontations in the future.
Meanwhile, Israel's defence minister has testified before an internal Israeli commission investigating that raid.
Ehud Barak said he took full responsibility and that they had exhausted all other options before carrying out the operation.