Government considers request to be allowed to subpoena witnesses after panel’s request.
Eight Turks and a dual US-Turkish citizen were killed when Israeli commandos stormed the Turkish-flagged ship Mavi Marmara on May 31.
The deaths shattered bilateral ties already strained over Israel’s war on Gaza last year.
Turkey withdrew its ambassador to Israel, cancelled joint military operations and barred Israeli military aircraft from Turkish airspace after the incident.
The talks, which were made public by Israel and Turkish media reports, sparked a major row between the Israeli foreign ministry and the office of Benjamin Netanyahu, the prime minister.
Avigdor Lieberman, the foreign minister, said he had only heard about the meeting through the media and this could cause “serious harm” to relations with Netanyahu.
“The foreign minister views as extremely serious the fact that this was done without notifying the foreign ministry,” the ministry said in a statement.
“This goes against all norms of government and does serious harm to the trust between the foreign minister and the prime minister.”
Netanyahu’s office promptly issued a statement saying the fact that Lieberman had not been informed was a “technical” oversight.
Turkish officials have said Turkey expects Israel to apologise for the bloodshed on the Mavi Marmara, compensate the victims’ families, agree to an international inquiry and release three Turkish vessels seized in the operation.
Turkey also wants Israel’s 2003 blockade of Gaza to be lifted.
Israel, which strictly controls Gaza’s borders in what it says is a precaution against arms smuggling, has defended the actions of marines who boarded the ship, arguing they opened fire after being attacked with knives and clubs.
But following international criticism, including from its largest ally the United States, Israel has eased a land blockade of Gaza where 1.5 million Palestinians live, allowing more civilian goods through, while continuing to enforce a naval embargo of the coastal territory.
On Monday, Israel launched a commission of inquiry into the raid, although the panel’s make-up and limited powers have been criticised by Turkey.