Obama said Wednesday he was authorizing U.S. airstrikes inside Syria and expanded strikes in Iraq. He also again asked Congress to authorize a program to train and arm Syrian rebels who are fighting both Islamic State militants and forces of Syrian President Bashar Assad.
"I thought that the president made a very strong statement last night about the threat posed by ISIL, a very compelling argument about the need to combat that threat, and a good point of departure," Petraeus said, using one of the acronyms for the Islamic State group.
"Do not underestimate the Iraqi security forces," he said. Some of their problems were political and were resolved with the new government.
The Islamic State militants do not have strong local support in Iraq and their strength should not be over-rated, he said.
Petraeus said the current crisis in Iraq is serious but not as desperate as the situation in December 2006, when Petraeus commanded a buildup in U.S. forces ordered by then-President George W. Bush.
The situation in Syria is different, he said, with no unified army to push the Islamic State fighters back under the cover of U.S. fighter jets. Petraeus did not comment on the proposal to arm Syrian rebels.
Asked whether the Islamic State militants hoped to draw the U.S. into greater involvement by beheading two American journalists, Petraeus said, "If someone has a death wish, he's expressed it quite effectively."