"The current closure is unacceptable and counterproductive," Grant said.
France, Russia and China also called for the blockade to be lifted and for an independent inquiry.
The United States, Israel's traditional ally, did not request specifically that Israel end its blockade on the Gaza Strip. But it hinted that the measure at least should be eased.
Alejandro Wolff, US deputy permanent representative, said that Washington was "deeply disturbed by recent violence and regrets tragic loss of life and injuries".
Meanwhile the EU and Russia have issued a joint condemnation of Israel's use of deadly force in the operation, and urged the opening of crossings in Gaza.
Speaking during a Russia-EU summit, Sergei Lavrov, the Russian foreign minister and Catherine Ashton, the EU foreign policy chief demanded an end to the blockade of Gaza.
Their joint declaration added: "The EU and Russia call for immediate opening of crossings for the flow of humanitarian aid, commercial goods and people to and from Gaza."
The EU's president, Herman Van Rompuy, called for a "durable solution" for the situation in Gaza. "We regret the loss of life, condemn the use of violence and demand an immediate, full and impartial investigation," he said.
Dmitry Medvedev, Russia's president, said that the civilian deaths were "irreparable and aboslutely unjustified."
Meanwhile, Egypt opened its Rafah border crossing with the Gaza Strip letting Palestinians cross until further notice.
Palestinian TV said that Mahmood Abbas, the president, phoned Hosni Mubarak, his Egyptian counter-part, to thank him for "responding to the massacre" by opening the post.
The statements reflected the international community's strong disapprovalof Monday's events in the high seas, when Israeli soldiers stormed the six ships in international waters about 65km off the Gaza coast.
The ships with about 700 pro-Palestinian activists were carrying 10,000 tonnes of humanitarian aid for Gaza, the coastal territory under a crippling Israeli siege.
Israel insisted that its troops had acted in self-defence after being attacked by those onboard.
But Al Jazeera's Jamal Elshayyal, onboard the lead ship Mavi Marmara, said troops opened fire even after passengers had raised a white flag.
Israeli troops have taken the ships to the port of Ashdod after seizing them.
Activists who were injured are being treated in hospitals while 480 others are been detained and subjected to interrogations. Another 48 activists have been deported to their respective countries.
Al Jazeera's Elshayyal is reportedly being held at a detention facility at Tel Aviv's Ben Gurion airport, together with two of his colleagues.
Al Jazeera's Ayman Mohyeldin, reporting from Ashdod, said: "We are still trying to get information in terms of the condition of the passengers...
"An identification and interrogation process has gotten under way, to identify the individuals and then provide them with the option of being deported immediately or sent to prison here," he said.
Freedom Flotilla has incensed people, triggering mass protestsin cities across the world.
Thousands marched in the streets of Istanbul, London and Amman in Jordan among other cities on Monday, denouncing the deadly raid on the ships that sought to deliver much-needed supplies to Gazans.
But Israel has remained defiant with Mark Regev, its government spokesman, insisting that "Israel was totally within its rights under international law to intercept the ship and to take it to the port of Ashdod".
He said the people on board the flotilla were not peaceful activists.
"They are part of the IHH, which is a radical Turkish Islamist organisation which has been investigated by Western governments and by the Turkish government itself in the past for their links with terrorist organisations."
Reporting from Jerusalem, Al Jazeera's Jacky Rowland said Israel's reaction has largely been of defiance.
"Many [Israeli citizens] have flocked to the port of Ashdod to basically express their rejection of what they see as the foreign media's negative spin on events.
"...Israeli spin masters have been going into overdrive, doing their best possible to spin this event as though the Israeli commandos were not the ones attacking but rather the attack was perpetrated by people on board," she said.
But Israeli efforts notwithstanding, the country has come in for strong censure.
||Two Palestinians who are also members of Israeli parliament
||Swedish author Henning Mankell (unharmed according to the Swedish foreign ministry)
||Northern Irish Nobel peace prize laureate Mairead Maguire
||Aengus Snodaigh, member of the Irish parliament
||Irish writer and historian Fintan Lane
||Three German parliamentarians
Murat Mercan, the head of Turkey's foreign relations committee, said claiming that activists on board had links to terrorist organisations was Israel's way of covering up its mistake.
"Any allegation that the members of this ship is attached to al-Qaeda is a big lie because there are Israeli civilians, Israeli authorities, Israeli parliamentarians on board the ship," he told Al Jazeera.
"Does he [Regev] think that those are also attached to al-Qaeda?"
Mark Taylor, an international legal expert, told Al Jazeera that every state, including Israel, has the right to self-defence.
"In this case, we're looking at a humanitarian aid convoy, with prominent people and activists, clearly not a military target in any way whatsoever."
Israeli media reported that many of the dead were Turkish nationals.
Hamas, the Palestinian group which governs the Gaza Strip, said the assault was a "massacre" and called on the international community to intervene.
The Hamas leader in Gaza, Ismail Haniya, urged Arabs and Muslims to show their anger by staging protests outside Israeli embassies across the globe.