"The prime minister said Israel would not cooperate with any commission that would ask to question soldiers," spokesman Nir Hefetz told military radio.
"Before Israel gave the green light to its participation in the panel we had discreet negotiations in order to ensure that this commission would not harm the vital interests of Israel," he added.
Ban on Monday denied there was such an agreement.
The row broke out as the UN commission was due to start work, and on the second day of a series of top-level hearings by an Israeli panel, which also does not have the authority to question the soldiers who stormed the ships.
Testifying in Jerusalem, Defence Minister Ehud Barak said the flotilla was a "planned provocation" and that top officials had suspected more than a month beforehand that organisers were "preparing for an armed conflict to embarrass Israel."
He said various alternatives were discussed ahead of the raid and that he and other senior officials had considered the possibility that the activists would attack the troops when they landed.
"We regret any loss of life," the minister told the Tirkel Commission, a panel of five Israelis and two international observers charged with examining the international legality of the raid and the Gaza blockade.
"But we would have lost more lives if we had behaved differently."
Netanyahu told the panel on Monday that Israel had acted in line with international law, and accused Turkey of seeking a high-profile confrontation that saw activists attack its commandos with iron bars and knives.
The bloody raid caused a diplomatic crisis between Israel and Turkey.
"Turkey remains a very important state in the Middle East. We have to find a way ... to rectify the deterioration of relations," Barak said on Tuesday.
But he stressed that the naval blockade is "absolutely essential to stop Gaza from transforming into a massive arsenal. It is designed to stop the transfer of rockets and other means of warfare."
Israel imposed border restrictions in June 2006 after Gaza militants captured an Israeli soldier. The sanctions, which have been largely backed by neighbouring Egypt, were tightened in June 2007.
In 2009 Israel formally declared a naval blockade, which Barak claimed allows Israel under international law to interdict Gaza-bound vessels.
The results of an internal military investigation, which are to be submitted to the Tirkel Commission and the UN panel, found that mistakes were made at a "relatively senior" level but that the use of live fire was justified.
Israel says its commandos resorted to force only after they were attacked when they rappelled onto the deck of one of the ships, but pro-Palestinian activists on board say the soldiers opened fire as soon as they landed.
Armed forces Chief of Staff Gabi Ashkenazi was to take the stand on Wednesday and was likely to be quizzed over the operational aspects of boarding the ships.
Last week Ban named his own panel, chaired by former New Zealand prime minister Geoffrey Palmer, to look into the deadly raid. It was due to begin work on Tuesday and includes representatives from Israel and Turkey.
Israel has completely rejected a separate investigation launched by the UN Human Rights Council, which it views as hopelessly biased against the Jewish state.