French President Francois Hollande has said nations owed it to the sacrifice of those who took part in the D-Day landings to build "a fairer world".
Paying tribute to the courage of troops 70 years ago, he said their spirit will always be felt on the Normandy beaches, where they came ashore.
And Mr Hollande said the appreciation of France to the liberating forces "will never die".
Normandy veteran Ken Scott, 98, remembers his fallen comrades
War veterans arrive for the service at Bayeux Cathedral
He was speaking at the main ceremony at Sword Beach in Ouistreham, to commemorate the 70th anniversary of history's biggest amphibious invasion.
Veterans, politcians and members of the Royal Family including the Queen had gathered in Normandy to mark the events of June 6, 1944.
The D-Day operation, involving 150,000 Allied troops, changed the course of the Second World War.
Soldiers landing on Juno Beach in Bernieres-sur-Mer on June 6, 1944
Mr Hollande said: "We have to be faithful to their sacrifice to build in their name, and the name of future generations, a fairer world and a more human world."
He also said freedom is a fight, and continued to be threatened around the world.
"There are always men and women who have to get up and defend freedom," he said.
The Queen joined world leaders to mark the 70th anniversary
Mr Obama applauds US veterans during the ceremony in Colleville-sur-Mer
The same courage shown by the troops on D-Day must now be shown in defeating the "ills" of the modern world, including terrorism, and crimes against humanity.
Earlier, David Cameron had also called for leaders to set aside their differences on the "incredibly moving" anniversary of the landings.
The events of D-Day "show the importance of standing up together ... for freedom and security", he said.
Vintage US military vehicles are driven along Gold Beach
Described by wartime Prime Minister Winston Churchill as "undoubtedly the most complicated and difficult (operation) that has ever taken place", D-Day proved to be a pivotal moment of the Second World War.
It marked the start of an 80-day campaign to liberate Normandy, that involved three million troops and cost some 250,000 lives.
Services marking their sacrifice were held at beaches and war cemeteries across the region.
Cemeteries along the French coast are a focal point for the commemorations
A British veteran walks past a line of gravestones for fallen soldiers
In Colleville-sur-Mer, Barack Obama joined Mr Hollande for a service at the Normandy American Cemetery and Memorial, where more than 9,000 soldiers are buried.
"These men waged war so that we might know peace, they sacrificed so that we may be free, they fought in hope of a day that we would no longer need to fight and we are grateful to them," the US President said.
In nearby Bayeux, the Queen and the Duke of Edinburgh visited the Commonwealth War Graves cemetery, where 4,144 soldiers, 338 of them unidentified, are buried.
Further along the coast in Arromanches, the Normandy Veterans' Association had organised a day of events.
This anniversary will be the group's last as it plans to disband later this year.
Commemorations began at midnight when Mr Cameron attended a memorial at Pegasus Bridge, the first strategic landmark to be captured.
At the exact time the first gliders landed, a champagne toast was raised at Cafe Gondree, the restaurant next to the bridge, which became the first house to be liberated in France.
American veterans gathered at dawn on Omaha Beach, where a statue of two soldiers was unveiled.