Al Libi “helped plan and execute plots that killed hundreds of people, a whole lot of Americans. We have strong evidence of that. And he will be brought to justice,” Obama told reporters in a news conference.
The Al Qaeda figure was captured in Tripoli on Saturday  and then taken onto a Navy ship in the Mediterranean Sea.
Al Libi is being questioned by the US High Value Detainee Interrogation Group, an inter-agency group created in 2009 and housed in the FBI's National Security Branch, according to Reuters.
He is a suspect in the 1998 bombings of the US embassies in Kenya and Tanzania that killed 224 civilians  and is on the FBI’s most wanted list with a $5 million reward.
The Al Qaeda suspect has been accused in a US federal court in New York for allegedly playing a key role in the East Africa bombings.
Libya has condemned Al Libi’s capture and demanded on Tuesday that the United States hand him back , describing the US operation as a "flagrant violation of (Libya's) national sovereignty," AFP reported.
The government has also summoned US Ambassador Deborah Jones to seek clarification over the capture.
Obama, who was speaking at the White House in the midst of the partial government shutdown, also said the United States will continue to go after Al Qaeda-linked groups in Africa. But this is not similar to going to wars, he said.
“Where you've got active plots and active networks, we are going to go after them ,” Obama said, according to Reuters.