"As long as I am Commander in Chief, I am going to do right by them. American will not let you down, we will take care of our own," he said.
He also honoured those soldiers still fighting in Iraq and Afghanistan, saying they already deserve "a place alongside previous generations for the courage they have shown and the sacrifices they have made".
Following the speech, he walked among the section of the cemetery reserved for those who had died fighting in the two conflicts.
Mr Obama is due to meet members of his security team later to discuss a new strategy for US involvement in Afghanistan.
The BBC's Kevin Connolly in Washington says a decision is expected within weeks, and is almost certain to involve sending tens of thousands more US troops to the country to tackle the Taliban insurgency.
At Armistice Day events in Paris, Mrs Merkel and French President Nicolas Sarkozy rekindled the flame on the Tomb of the Unknown Soldier at the foot of the Arc de Triomphe.
WORLD WAR I
28 Jul 1914: Austria-Hungary declares war on Serbia
1914-17: Major world powers enter war, stalemate of trench warfare on Western front
The two leaders also observed a silence, flanked by soldiers from a Franco-German brigade and officers from both countries' armed forces.
Mr Sarkozy told Mrs Merkel her presence was "a gesture of exceptional friendship" while Mrs Merkel said she thanked history for bringing the two former enemies together.
In London, the Queen led the United Kingdom in observing a two-minute silence at 1100 GMT for the "passing of a generation".
The service in Westminster Abbey followed the deaths this year of the final three veterans of World War I living in the UK.
In the Belgian town of Ypres, poppy petals - the symbol of Armistice Day - were dropped from the Menin Gate, on which the names of 55,000 missing WWI soldiers are engraved.
Australia's east coast, which is 11 hours ahead of GMT, was one of the first places to commemorate the 11th hour of the 11th day of the 11th month - the time the guns of WWI fell silent.
The names of five Australian soldiers killed in Afghanistan since Remembrance Day last year were being added to the roll of honour at the Australian War Memorial in the capital, Canberra, Australian television reported.
This page is best viewed in an up-to-date web browser with style sheets (CSS) enabled. While you will be able to view the content of this page in your current browser, you will not be able to get the full visual experience. Please consider upgrading your browser software or enabling style sheets (CSS) if you are able to do so.