Barak gave no details of the format of such a probe, which Israeli media reports said was still being worked out.
He also suggested Israel was also looking at ways to amend its four-year blockade on the Gaza Strip, although he added it would maintain restrictions it sees as essential to preventing Iranian missiles from reaching the Palestinian territory.
Barak said the planned investigation would run separately from the military investigation, and would seek to establish whether Israel's blockade of Gaza and its raid "met with the standards of international law".
"We will draw lessons at the political level, (and) in the security establishment," he said.
The announcement of the Israeli investigations came as Turkey's prime minister reiterated calls for an immediate international inquiry into the Israeli commando raid on the Gaza-bound flotilla.
|Israel has rejected calls for an international investigation into the raid [Reuters]
Speaking on the first day of an Asia security summit in Istanbul, Recep Tayyip Erdogan said the Israeli attack was "unlawful" and required a UN backed "transparent" investigation.
"We believe that an independent inquiry ... to investigate this unlawful incident in a very transparent and fair manner ... has to be initiated as soon as possible," Erdogan said.
"We will be following that up and we would like to ask the UN to pursue this matter to the end."
Eight of those killed in the raid were Turkish citizens, while the other had dual US-Turkish citizenship.
Erdogan made his comments at a joint news conference with Bashar al-Assad, Syria's president.
"The time has come to lift the embargo on Gaza," said the Turkish prime minister.
"We don't want an open air prison in the world any more."
Al-Assad echoed Erdogan's call for an investigation as well urging an end to the Israeli blockade of Gaza, which began in 2007.
|Turks have been outraged by the Israeli raid
on the aid flotilla [Reuters]
"As a minimum we should see the establishment of a neutral investigation committee in addition to lifting the blockade," al-Assad said.
"If blood was shed for a certain objective we should make everything possible to achieve their objective [to break the blockade] and we should continue in our efforts on this path."
Erdogan and al-Assad were speaking on the opening day of a two-day summit on security in Asia.
Turkey said Israel, also a member, was invited but was not expected to be at the Conference on Interaction and Confidence Building Measures in Asia.summit.
Anita McNaught, Al Jazeera's correspondent in Istanbul, said Erdogan is looking for partners in the region to take action against Israel.
"What this regional security summit is about is Turkey figuring out what partners it has if it moves to try and isolate Israel, politically, economically, militarily, however it can," she said.
Turkey had a solid alliance with Israel until the Gaza war in early 2009.
Following last week's attack, Ankara said it would reduce its military and trade ties with Israel and has shelved discussions on energy projects, including natural gas and fresh water shipments.
It has also threatened to break ties unless Israel apologises for the raid.
Speaking on the sidelines of the conference in Istanbul, Ahmet Davutoglu, Turkey's foreign minister, said his country was "evaluating everything".
"It is up to Israel how our ties will continue," he said.
"Israel has to accept the consequences of its actions and be held accountable".