In an interview to British television network Sky News, which will be aired Sunday, Obama refused to explicitly address Syrian President Bashar Assad's invitation to him to visit Damascus and discuss regional peace.
The US president clarified that his administration still had some reservations in regards to Syria.
"I think that we've started to see some diplomatic contacts between the United States and Syria," he said, but clarified that most of the problems between the two countries still stand.
"There are aspects of Syrian behaviour that trouble us and, you know, we think that there is a way that Syria can be much more constructive on a whole host of these issues," he explained.
Obama refrained from directly addressing Assad's public invitation, but expressed his optimism over the chances of making progress in the relations between the two countries. "I'm a believer in engagement and my hope is that we can continue to see progress on that front," he added.
Last week, Assad invited Obama to visit Damascus for a summit in which the two leaders would discuss peace efforts in the Middle East.
Assad told Sky News that he would be happy to meet with Obama on Syrian soil, and that the date of the meeting was up to the Americans to decide.
"We would like to welcome him in Syria, definitely. I am very clear about this," Assad told Sky's Middle East correspondent. Asked whether this could happen soon, the Syrian president said, "That depends on him."
Assad's comments come a day after his British-born wife Asma told Sky News that she envisioned welcoming Obama and his wife Michelle to Damascus.
The Syrian first lady estimated that there was a reason for hope following the change of guards in Washington. "The fact is President Obama is young, and President Assad is also very young as well, so maybe it is time for these young leaders to make a difference in the world."