UN Security Council members condemned Israel as they began an emergency session over Israel's deadly raid on a flotilla of ships carrying aid to Gaza.
At least nine pro-Palestinian activists, some Turkish, were killed when Israeli commandos stormed the ships in international waters.
Turkey's foreign minister called Israel's actions "murder by a state".
Israel's UN envoy said troops acted in self-defence when activists attacked them, charges the campaigners deny.
"This flotilla was anything but a humanitarian mission," Israel's deputy UN ambassador Daniel Carmon said.
He said the activists had used "knives, clubs and other weapons" to attack the soldiers who boarded the lead boat, the Mavi Marmara.
The campaigners insist the soldiers opened fire without any provocation.
Injured activists have been taken to Israeli hospitals, while dozens of others have been detained and are being processed for deportation.
Israel has imposed an information blackout, making it difficult to gather first-hand accounts from the campaigners.
The ships were carrying 10,000 tonnes of aid in an attempt to break Israel's three-year blockade of the Gaza Strip.
The Security Council's emergency session continues behind closed doors at the UN headquarters in New York.
Member states are debating a possible reaction to Israel's killing of the nine pro-Palestinian activists in international waters.
Most of the activists killed are believed to have been Turkish, and Turkey led a chorus of criticism of Israel at the UN.
"In simplest terms, this is tantamount to banditry and piracy. It is murder conducted by a state," Turkish Foreign Minister Ahmet Davutoglu said ahead of the session.
Mr Davutoglu told the BBC that Israel must issue an immediate apology for its storming of the aid ship and repatriate the pro-Palestinian campaigners.
None of the other 15 members of the Security Council was as outspoken in their individual statements, but most called for a full investigation and were critical of Israeli actions.
Many - including veto-wielding members France, Russia and China - also demanded an end to the Israeli blockade on Gaza which the aid ships were trying to break.
Israel's closest ally, the United States, expressed concern, although deputy US ambassador to the UN Alejandro Wolff said it was still not clear what had happened.
"The US is deeply disturbed by the recent violence and regrets the tragic loss of life and injury suffered among those involved in the incident last night, aboard the Gaza-bound ships," he said.
US state department spokesman Philip Crowley later said America "deeply regretted" the loss of life and expected a "full and credible" investigation by Israel.
UN Secretary General Ban Ki-moon has also called for a full inquiry.
Based on the stated positions of Security Council members, it is difficult to see how they can agree on a consensus statement, but that is what they are trying to do now behind closed doors, the BBC's Barbara Plett reports from the UN headquarters.
Diplomats say the draft text condemns the Israeli raid, requests immediate release of the impounded ships, and calls for an international investigation, our correspondent says.
Washington will face pressure to join the international condemnation of Israel, she adds.
There have been demonstrations against the Israeli operation in cities around the world, and several countries summoned their Israeli ambassadors demanding an explanation for the violence.
Palestinian President Mahmoud Abbas has condemned the Israeli "massacre" and declared three days of mourning across the West Bank.
The Arab League has called for an emergency meeting on Tuesday, as Jordan and Egypt - the two Arab states with peace deals with Israel - sharply condemned the violence.
For many critics of Israel - on the streets and in foreign ministries - it is not just about this single incident at sea, serious and deadly though it was, says the BBC's Jeremy Bowen in Jerusalem.
It is about a pattern of violent and disproportionate behaviour, with Israel playing to its own rules rather than international law, our correspondent says.
Israeli Defence Minister Ehud Barak told the BBC that Israel did not want to harm innocent civilians in Gaza, but had to fight the militant group Hamas which controls Gaza.
Israel imposed the blockade on the Gaza Strip after Hamas took power there in 2007.
Earlier, Israeli Prime Minister Benjamin Netanyahu said he regretted any loss of life, but gave full backing to the action of the Israeli troops.
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.
The six-ship convoy left Cyprus on Sunday to carry 10,000 tonnes of aid to Gaza, despite repeated Israeli warnings that it would not be allowed to reach the territory. It was due to arrive on Monday.
Reports say soldiers boarded the ships about 40 miles (64km) out to sea.
In Tel Aviv, Israel's navy commander said the troops took over five boats without incident and that all of the violence was centred on the Mavi Marmara.
Organisers of the flotilla said at least 30 people were wounded in the incident. Israel says 10 of its soldiers were injured, one seriously.
Israel has escorted the ships to the port of Ashdod and says it will detain or 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.