Obama became the first US president to formally acknowledge the victims of the 1976-1983 military regime, which declassified documents have revealed was supported by top US officials.
"There's been controversy about the policies of the United States early in those dark days, and the United States, when it reflects on what happened here, has to examine its own policies as well, and its own past," Obama said yesterday.
He spoke at Remembrance Park, a monument in Buenos Aires to the 30,000 people who were killed or went missing under the dictatorship. He paid tribute to victims' families.
Tens of thousands of people joined a noisy demonstration later in Buenos Aires to mark the 40th anniversary of the US-backed coup that brought the dictators to power.
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They marched to the din of drums, carrying pictures of victims. Similar anniversary marches were called in towns across the country.
Some rights groups complained Obama had not gone far enough.
"The self-criticism was totally light," said Taty Almeida, founder of the victims' campaign group Madres Linea Fundadora.
Victims' groups had been angered by the choice of the date for Obama's visit, given the US support for the coup at the time.
But they welcomed his promise to declassify further documents to shed more light on the fates of the regime's victims.
After the memorial ceremony Obama with his wife Michelle, her mother and the couple's daughters flew to the Andean resort of Bariloche, where they went for a hike and boat ride in a national park.
Early today, the Obamas left Argentina to return home to Washington.