"I expect that by early next year we may even have fewer than a hundred people at Guantanamo," Obama said during a visit to Manila.
Obama has repeatedly tried to close the facility - which currently houses 107 inmates - but has been thwarted by opposition in Congress.
The White House has promised to produce a fresh plan soon to transfer the remaining prisoners to foreign countries, or the United States.
As a candidate and as US president, Obama has argued that indefinite detention, "enhanced interrogation" and images of caged men in orange jump suits violated America's ethos and handed militants a potent recruiting tool.
But ensconced in the Oval Office, he quickly became ensnared in a legal and political thicket.
Obama rejected suggestions he had abandoned efforts to push forward a plan, saying the administration would "work diligently" to complete it.
The White House has hinted that it may resort to controversial executive orders if Congress refuses to act.
Republicans have vowed to block the confirmation of administration appointees and take other punitive measures if Obama moves forward.
"We are going to go through, meticulously, with Congress, what our options are, why we think this should be closed," Obama said. "I guarantee you there will be strong resistance.
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