"This is something that is going to require America's attention," Obama said during an interview broadcast Friday.
However, the president said the notion that the U.S. alone can end Syria's bloody civil war is "overstated" and made clear he would seek international support before taking large-scale action.
"If the U.S. goes in and attacks another country without a U.N. mandate and without clear evidence that can be presented, then there are questions in terms of whether international law supports it, do we have the coalition to make it work," he said in the interview on CNN's "New Day" show. "Those are considerations that we have to take into account."
Obama's comments on Syria were his first since Wednesday's alleged chemical weapons attack on the eastern suburbs of Damascus that killed at least 100 people. While he appeared to signal some greater urgency for a U.S. response, his comments were largely in line with his previous statements throughout the two-year conflict.
The president said the U.S. is still seeking conclusive evidence that chemical weapons were used this week. Such actions, he said, would be troubling and detrimental to "some core national interests that the United States has, both in terms of us making sure that weapons of mass destruction are not proliferating, as well as needing to protect our allies, our bases in the region."
Wednesday's attack came as a United Nations team was on the ground in Syria investigating earlier chemical weapons use. Obama has warned that deployment of the deadly gases would cross a "red line," but the U.S. response to the confirmed attacks earlier this year has been minimal.
That has opened Obama up to fierce criticism, both in the U.S. and abroad. Among the critics is Arizona's Republican Sen. John McCain, who says America's credibility has been damaged because Obama has not taken more forceful action to stop the violence. McCain ran against Obama for president in 2008.
The president pushed back at those assertions in the interview aired Friday, saying that while the U.S. remains "the one indispensable nation," that does not mean the country should get involved everywhere immediately.
"Well, you know, I am sympathetic to Sen. McCain's passion for helping people work through what is an extraordinarily difficult and heartbreaking situation, both in Syria and in Egypt," he said.
"Sometimes what we've seen is that folks will call for immediate action, jumping into stuff, that does not turn out well," he said. "We have to think through strategically what's going to be in our long-term national interests, even as we work cooperatively internationally to do everything we can to put pressure on those who would kill innocent civilians."
The U.S. has called on Syria to allow the U.N. team currently on the ground to investigate this most recent attack. However, the president was pessimistic about those prospects, saying, "We don't expect cooperation, given their past history."
More than 100,000 people have been killed in Syria during more than two years of clashes between forces loyal to Syrian President Bashar Assad and opposition fighters seeking to overthrow his regime. The U.S. has long called for Assad to go and has sent humanitarian aid to the rebels, but those steps have failed to push the Syrian leader from power.
After the earlier chemical weapons attacks, Obama did approve the shipment of small weapons and ammunition to the Syrian rebels, but there is little sign that the equipment has arrived.
Obama addressed the deepening crisis in Syria from central New York, where he is on a two-day bus tour promoting policies to make college more affordable.