"It is clearer than ever that Israel's restrictions on access to Gaza must be lifted in line with Security Council Resolution 1860. The current closure is unacceptable and counterproductive," British Ambassasdor Mark Lyall Grant said ahead of the emergency session called after the deadly attack.
France, Russia and China -- veto-wielding permanent council members -- also called for the blockade to be lifted and for an independent inquiry.
The United States, Israel's traditional ally which often uses its veto power to aid the Jewish state -- did not request specifically that Israel end its blockade on the Gaza Strip. But it hinted that the measure at least should be eased.
US deputy permanent representative Alejandro Wolff said Washington was "deeply disturbed by recent violence and regrets tragic loss of life and injuries. We are working to ascertain the facts.
"We expect a credible and transparent investigation and strongly urge the Israeli government to investigate the incident fully," Wolff said.
"Direct (aid) delivery by sea is neither appropriate nor responsible under the circumstances," Wolf added noting that the "situation (was) unsustainable and is not in the interest of any of those concerned.
"We will continue to engage the Israelis on a daily basis to expand the scope and type of goods that are allowed into Gaza," Wolff said.
Israel's UN envoy Daniel Carmon meanwhile insisted that the flotilla was not on an aid mission.
"Although portrayed in the media as a humanitarian mission delivering aid to Gaza, this flotilla was anything but a humanitarian mission," Carmon said.
"What kind of humanitarian activists demand to bypass the United Nations, the Red Cross, and other internationally recognized agencies?
"What kind of peace activists use knives, clubs and other weapons to attack soldiers who board a ship in accordance with international law?"
The Brazilian UN envoy Maria Luiza Ribeiro said the incident "stresses the need for the blockade of Gaza to be lifted. It is a violation of international law," she said.
For Wolf, the US diplomat, "ultimately this incident underscores the need to move ahead quickly with negotiations that can lead to a comprehensive peace in the region.
"The only viable solution to the Israeli-Palestinian conflict is an agreement negotiated between the parties that ends the occupation that began in 1967 and fulfills the aspirations of both parties for independent homelands for two States."
Israel is facing a wave of international condemnation over the raid, in which at least nine people were killed.
Yahya Mahmassani, representing the Arab group at the UN, said there were a number of issues that were important for Council members to address.
"We want a strong condemnation because this happened in international waters, two: we want to lift the blockade on Gaza, to allow all the food and material that was sent to Gaza to arrive and third: Israel should abide by international law and its commitment under international law," he told AFP.
The talks were requested by Lebanon, which holds the council's rotating presidency until 0400 GMT on Tuesday.
The country's Prime Minister Saad Hariri "asked the Lebanese delegation at the UN to call for an emergency meeting over what happened today," a Lebanese official told AFP earlier.
The Palestinian permanent representative to the world body, Riyad Mansour, said there was hope that "at the end of the day... the Security Council will have a decisive outcome, a reaction to bring Israel into account at the same level of that crime that has been committed in the high seas."
Turkish Foreign Minister Ahmet Davutoglu said: "Israel's action is a grave breach of international law. In simpler terms, it's tantamount to banditry and piracy. It's murder conducted by a State."
------------------------------------------------------------------------------