Hours after the barrage of airstrikes began, Lt Gen William Mayville said the attacks took out key Islamic State training camps and facilities.
But he said it was too early to tell if they were able to disrupt a terrorist attack being planned by al-Qaida militants, known as the Khorasan Group.
"We're going to do what's necessary to take the fight to this terrorist group, for the security of the country and the regime and for the entire world," Obama said as he left Washington for meetings of the UN General Assembly in New York.
Army Gen Martin Dempsey, the top American military official, said the US and its Arab allies achieved their aim of showing the extremists that their attacks will not go unanswered.
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Gen Mayville, director of operations for the Joint Chiefs of Staff, said at the Pentagon that the US carried out the vast majority of the strikes in an operation against the Islamic State group that he said would continue and likely last "in terms of years."
But he declined to provide details on what the Arab nations did. He said the strikes included Islamic State militants' financial centers in order to disrupt the well-funded group's activities.
Rami Abdurrahman, who heads the Britain-based Syrian Observatory for Human Rights, told The Associated Press, "There is confirmed information that there are casualties among Islamic State group members."
The strikes weren't coordinated with the government of Syrian President Bashar Assad, Mayville said, but Syrian and US officials said that the US informed Syria's envoy to the UN ahead of time.