About 700 people from more than 30 countries were aboard the six ships that were raided, with 380 activists believed to be Turkish.
At least four of those killed in the attack were Turkish nationals.
In a speech to legislatorson Tuesday, Erdogan said: "It is no longer possible to cover up or ignore Israel's lawlessness.
"The international community must from now on say 'enough is enough'.
"Dry statements of condemnation are not enough ... there should be results."
Anita McNaught, Al Jazeera's correspondent in Istanbul, said Erdogan's speech was "extraordinarily strong".
She said he "mentioned the unmentionable, saying that Israel acts because it has powerful friends".
Turkey called for a strong international response to the raid, with Erdogan saying he would be speaking to Barack Obama, the US president, later in the day.
The ships were carrying 10,000 tonnes of humanitarian aid for Gaza when they were boarded by Israeli commandos.
Israel says its troops, who took the ships to the port of Ashdod after seizing them, acted in self-defence after being attacked by those on board.
Activists who were injured are being treated in hospitals while 480 others have been detained and subjected to interrogations.
Another 48 activists have been deported to their respective countries.
The Israeli government said on Tuesday that it would hand over 124 activists to Jordan later in the day.
Anders Fogh Rasmussen, the Nato secretary general, called on Israel on Tuesday to immediately release those people and boats still held after the raid.
Rasmussen, speaking after an emergency meeting of the military alliance requested by Turkey, said: "As a matter of urgency, I ... request the immediate release of the detained civilians and ships held by Israel."
France also demanded the immediate release of the activists.
"France demands the immediate release of the boats and of all the civilians who were on board," said Francois Fillon, the prime minister, noting that nine French nationals were among those held.
Earlier on Tuesday, the UN Security Council condemned the deaths caused by Israel's attack.
In a formal statement adopted after more than 10 hours of closed-door negotiations, the council requested the immediate release of ships and civilians held by Israel and called for an impartial investigation.
France, Russia, China and the UK also called for the blockade of Gaza to be lifted.
"It is clearer than ever that Israel's restrictions on access to Gaza must be lifted in line with Security Council Resolution 1860," Mark Lyall Grant, the British ambassador, said on Tuesday.
"The current closure is unacceptable and counterproductive."
The United States, Israel's traditional ally, did not request specifically that Israel end its blockade on of Gaza but it hinted that the measure should at least 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".
The statements reflected the international community's strong disapproval of Monday's events in the high seas, when Israeli soldiers stormed the six ships in international waters about 65km off the Gaza coast.
Al Jazeera's Jamal Elshayyal, on board the lead ship Mavi Marmara, said troops opened fire even after passengers had raised a white flag.
Elshayyal is reportedly being held at a detention facility at Tel Aviv's Ben Gurion airport, together with two of his colleagues.
Ayman Mohyeldin, Al Jazeera's correspondent in 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."