OMAHA BEACH, France — President Obama honored the valiant dead and the "sheer improbability" of their D-Day victory, commemorating yesterday's 65th anniversary of the decisive invasion even as he remakes two wars and tries to thwart potential nuclear threats in Iran and North Korea.

The young U.S. commander in chief, speaking at the American cemetery after the leaders of France, Canada and Britain, held up the sacrifices of D-Day veterans and their "unimaginable hell" as a lesson for modern times.

"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."

Obama opened the emotional day by meeting with French President Nicolas Sarkozy in the nearby city of Caen. Their wives, dueling style icons in similar attire, met separately at the elegant French Prefecture.

Appearing with Sarkozy before reporters, Obama displayed growing impatience with North Korea and what he called its "extraordinarily provocative" nuclear and ballistic missile tests. He suggested that the North is testing international patience as diplomacy has failed to persuade the reclusive communist government to abandon its nuclear weapons program.

"Diplomacy has to involve the other side engaging in a serious way in trying to solve problems," he said. "We are going to take a very hard look at how we move forward on these issues, and I don't think that there should be an assumption that we will simply continue down a path in which North Korea is constantly destabilizing the region and we just react in the same ways."

Obama also took on Iran, suspected by the West of seeking to build its first nuclear bomb, an accusation Tehran denies. The president has said military action remains on the table, but has offered to change U.S. policy and engage in talks with Tehran. He said yesterday, though, it must be "tough diplomacy."

"We can't afford a nuclear arms race in the Middle East," Obama warned. Sarkozy said he worries about "insane statements" by Iran's president, Mahmoud Ahmadinejad.

At the same time, Obama is directing wars in Iraq and Afghanistan — seeking to end the first and stepping up U.S. engagement in the second. Both have lasted longer than the U.S. involvement in World War II.

This D-Day anniversary assumed special significance because veterans of the battle are reaching their 80s and 90s and their numbers are dwindling. One American veteran, Jim Norene, who fought with the 101st Airborne Division, came back for yesterday's ceremony, but died in his sleep Friday night.

"Jim was gravely ill when he left his home, and he knew that he might not return," Obama said. "But just as he did 65 years ago, he came anyway. May he now rest in peace with the boys he once bled with, and may his family always find solace in the heroism he showed here."

Joined by Sarkozy, British Prime Minister Gordon Brown, and Canadian Prime Minister Stephen Harper, Obama stopped first at the gray granite visitors center and then at an overlook where the leaders talked at length with two D-Day veterans waiting at the top of the once-bloody bluffs.

The sunny sky, crashing waves, lush vegetation and pleasant breezes created a scene of seaside tranquility at the spot one D-Day veteran recalled as mostly "darkness and confusion."

"I lost a lot of pals on D-Day," said Norman Coleman of Manchester, England. He marked the day by visiting several other burial grounds scattered around the region.

Julien Marchand, a 40-year-old carpenter, spontaneously embraced Coleman in an outburst of gratitude on the streets of Caen, nearly knocking over the elderly veteran. "Thank you, thank you, merci," Marchand exclaimed.

The ceremony at Omaha Beach, on what is technically U.S. soil at Colleville-sur-Mer, took place under an American flag flying from a metal pole hundreds of feet high. The crowd of thousands spread.

With clusters of young people sprinkled among the graying heads and wheelchairs, the audience spilled down the path that cut between some of the nearly 10,000 perfectly aligned white crosses that mark the graves of U.S. dead.

Allied forces charged the shores of five beaches on France's northern coast, facing German land mines, machine guns and heavy artillery.

Some 215,000 Allied soldiers, and roughly as many Germans, were killed or wounded during D-Day and the ensuing three months before the Allies captured Normandy, opening a path toward Paris that eventually took them to Germany and victory over the Nazis.