Israeli PM Benjamin Netanyahu has expressed regret after at least nine people died when troops stormed ships trying to break the Gaza blockade.
But he said soldiers had been defending themselves after they were "clubbed, beaten and stabbed".
Pro-Palestinian campaigners say the soldiers opened fire unprovoked when they landed on the aid-carrying ships.
There has been international condemnation of the loss of life, and the UN is holding an emergency session.
As the meeting of the UN Security Council got under way in New York, diplomats said the draft text of a resolution called for condemnation of the operation, the immediate release of the impounded ships and for an international inquiry.
Turkish Foreign Minister Ahmet Davutoglu called the incident "murder committed by a state" and said Israel had "lost all legitimacy".
But Israeli UN representative Daniel Carmon told the Security Council that some on board the ships had motives other than providing humanitarian assistance, and had tried to lynch Israeli soldiers.
Mr Netanyahu cut short a visit to Canada to deal with the growing crisis and cancelled a scheduled meeting in Washington with US President Barack Obama on Tuesday.
Israel imposed a blockade on the Gaza Strip after the Islamist movement Hamas took power there in 2007.
The six-ship convoy had set out to carry 10,000 tonnes of aid from Cyprus to Gaza, despite repeated Israeli warnings that it would not be allowed to reach the territory.
In a statement, Mr Netanyahu defended the Israeli operation, saying troops were attacked when they landed on the largest of the six ships in the flotilla.
"They were mobbed. They were clubbed, they were beaten, stabbed," he said.
"There was even a report of gunfire and our soldiers had to defend themselves, defend their lives or they would have been killed.
"Regrettably, in this exchange... people died. We regret this loss of life. We regret any of the violence."
Organisers of the convoy have strongly denied the Israeli account.
Contact with activists on the ships was lost after the raids and no first-hand accounts from them have yet emerged.
Arafat Shoukri, of the Free Gaza Movement (FGM) which helped organise the convoy, said those on board one ship had told them by telephone that Israeli helicopters had arrived.
"Then we started to hear screams, shouting, shooting everywhere," he said. "We heard some of them shouting 'We are raising the white flag, stop shooting at us'."
He said Israeli claims that activists had pistols and other weapons were "cheap propaganda".
Audrey Bomse, also of the FGM, told the BBC that the activists were "not going to pose any violent resistance".
The flotilla left the coast of Cyprus on Sunday and had been due to arrive in Gaza on Monday.
Reports say troops boarded the ship about 40 miles (64 km) out to sea in international waters.
Organisers of the flotilla said at least 30 people were wounded in the incident. Israel says 10 of its soldiers were injured, one seriously.
There has been widespread condemnation of the violence, with several countries summoning their Israeli ambassadors.
UN chief Ban Ki-moon said he was "shocked" and called for a "full investigation" into what happened.
The White House said the US "deeply regrets the loss of life" and was "currently working to understand the circumstances surrounding this tragedy".
There was a particularly strong response from Turkey, where many of the activists on the ships are from.
Turkish Prime Minister Recep Tayyip Erdogan accused Israel of state terrorism and violation of international law.
In Istanbul, thousands of protesters took part in an angry demonstration against Israel.
Turkey was Israel's closest Muslim ally but relations have deteriorated in recent years.
Greece has withdrawn from joint military exercises with Israel in protest at the raid on the flotilla.
The office of French President Nicolas Sarkozy said he condemned "the disproportionate use of force", while UK Foreign Secretary William Hague said there was "a clear need for Israel to act with restraint and in line with international obligations".
The BBC's Jon Donnison in Gaza says there has been widespread anger there with protests organised by Hamas.
Israel has escorted the ships to the port of Ashdod and says it will deport the passengers from there.
Israel says it allows about 15,000 tonnes of humanitarian aid into Gaza every week.
But the UN says this is less than a quarter of what is needed.