"The indications that this had not been properly investigated just recently was brought to my attention," Obama said.
"So what I've asked my national security team to do is to collect the facts for me that are known, and we'll probably make a decision in terms of how to approach it once we have all of the facts gathered up," Obama told CNN in an interview.
The inquiry stems from the deaths of up to 2,000 Taliban prisoners who had surrendered to the US-backed Northern Alliance in late 2001.
The fighters were in the custody of troops led by Gen. Dostum, a prominent Afghan warlord who has served as chief of staff of the country's post-Taliban army.
The New York Times had reported on Monday that top officials from the previous administration of president George W Bush discouraged separate probes by the Federal Bureau of Investigation, the State Department and the Pentagon.
They wanted to hush up the killing of up to 2,000 prisoners in 2001 because it was carried out by the forces of General Abdul Rashid Dostam, an Afghan warlord then on the Central Intelligence Agency's payroll, it said.
Asked whether he would support an investigation, Obama said, "I think that, you know, there are responsibilities that all nations have, even in war. And if it appears that our conduct in some way supported violations of laws of war, then I think that, you know, we have to know about that."
When the US invaded Afghanistan after the September 11, 2001, attacks, Dostum sided with the Americans and received military and CIA support to battle the Taliban.
The allegations against Dostum first surfaced in a 2002 Newsweek report, which cited a confidential UN memo saying the prisoners died in cramped container trucks while being transported from their Konduz stronghold in northern Afghanistan to Sheberghan prison, west of Dostum's stronghold at Mazar-e Sharif.
At the time, the Boston, Massachusetts-based group Physicians for Human Rights said it found a mass grave in nearby Dasht-e Leili, where witnesses said the bodies of Taliban prisoners were buried. The finding prompted US Gen. Tommy Franks, who led the invasion of Afghanistan, to support an investigation into the allegations.
But The New York Times, citing government officials and human rights groups, reported last Friday that the Bush administration "repeatedly discouraged efforts to investigate the episode."
Dostum, a key ally of Karzai, was reportedly living in exile in Turkey until last month, when he was reinstated to his post as defence minister.