Allied leaders have been paying tribute to veterans of D-Day, as they mark the 65th anniversary of the landings at a series of events in Normandy.
US President Barack Obama said the bravery and selflessness of a few changed the course of a whole century.
He was speaking alongside French, Canadian and UK leaders at the American cemetery near Omaha Beach, scene of fierce fighting on 6 June 1944.
The Allies suffered 215,000 casualties on D-Day and in the Normandy campaign.
Germany suffered similar losses as the Allies fought desperately up the beaches and into the French countryside to form a bridgehead.
'Symbol of America'
Speaking at the US war cemetery in Colleville-sur-Mer, overlooking Omaha Beach, Mr Obama said it was the sheer improbability of the D-Day victory that had made it so memorable.
The leaders recalled the sacrifices of the Allied troops at the landings
"Friends and veterans, what we cannot forget - what we must not forget - is that D-Day was a time and a place where the bravery and selflessness of a few was able to change the course of an entire century," he said.
"At an hour of maximum danger, amid the bleakest of circumstances, men who thought themselves ordinary found it within themselves to do the extraordinary."
Speaking before Mr Obama, French President Nicolas Sarkozy thanked the Allies for their efforts in liberating France and Western Europe, and the Americans in particular for their bravery at Omaha.
It's a great feeling to come here - my comrades though are buried over at Omaha
"I want to say thank you to the survivors of this tragedy who are here today with us... We owe you our freedom," he said.
"Because of the blood in your veins you are a symbol of the America we love."
British Prime Minister Gordon Brown and Canada's Stephen Harper also recalled the Allies' sacrifices in their speeches.
Britain's Prince Charles was in attendance after the US intervened in a cross-channel row over the lack of an invitation for Queen Elizabeth.
Veterans of the landings were among the invited audience. Mr Sarkozy awarded the French Legion d'Honneur, the country's highest military honour, to one American, one Briton, one Canadian and one Frenchman.
Mr Obama's great-uncle, Charles Payne, 84, who helped to liberate a concentration camp near Buchenwald, has also travelled to Normandy.
Obama and Sarkozy remember D-Day
"It's a great feeling ... to come here," said Austin Cox, 90, of Maryland, who landed on Omaha Beach as a sergeant with the 29th Division of the US 115th Infantry Regiment.
"My comrades though are buried over at Omaha," he said.
Mr Obama and his family have now returned to Paris and are visiting Notre Dame cathedral.
They are due to fly back to the US on Sunday.
Saturday's events began in Bayeux with a service of remembrance and commemoration organised by the Royal British Legion.
Mr Brown and his French counterpart, Francois Fillon, both laid wreaths inside Bayeux cathedral.
Mr Obama flew into Paris late on Friday after a brief trip to Germany in which he and Chancellor Angela Merkel toured the Buchenwald concentration camp.
Accompanied by Mr Sarkozy, he arrived in Caen with his wife, Michelle on Saturday at midday (1000 GMT).
Thronging crowds gave the US leader a rock star-style welcome and cheered as he went on an impromptu walkabout before a formal welcoming ceremony from a French military guard.
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