"We say to you now that our spirit is stronger and cannot be broken; you cannot outlast us, and we will defeat you," the President said.
Although he did not mention bin Laden or al Qaeda by name, "it was clear who he was talking to," said former White House counter-terror director Richard Clarke, an ABC News consultant.
Obama's speech appeared to be a direct response to bin Laden's audio message last week in which he questioned whether the U.S. "is capable to keep fighting us for more years".
"The majority of the U.S. people are happy to get rid of Bush, Bush left for his successor a heavy heritage, the hardest part of heritage is guerilla wars," said bin Laden.
But Obama seems to have risen to bin Laden's challenge.
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"He told al Qaeda you cannot inflict enough pain on us to stop us from coming after you," said Clarke, who served as an adviser to Obama during the campaign.
The President's speech also included a direct message "to the Muslim world" saying the U.S. seeks "a new way forward, based on mutual interest and mutual respect."
"The Obama administration intends to fight al Qaeda on an ideological basis," said Clarke.
The President also signaled an end to Bush administration policies of alleged torture, referring to the Founding Fathers and "the rule of law and rights of man."
"Those ideals still light the world, and we will not give them up for expedience's sake," the President said, without any direct reference to water boarding or other interrogation techniques approved by the Bush administration.