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.
Smiling, he added, "I will ask you to convey the invitation to him."
This invitation is a significant move on the part of Syria towards the new American administration, after years of hostility under the Bush administration.
"It's normal to have differences between different cultures, between different nations and states," Assad said. "But I think the United States has a special role as the greatest power."
The Syrian president stressed that this was an important move. "Any summit between any two presidents is something positive. That doesn't mean you have to agree about everything. But when you discuss, this is how we can close the gap."
Assad also said he was in favor in principle of renewing indirect talks with Israel, provided the right mediator could be found.
Asma Assad: World belongs to young people
Assad's comments come a day after his British-born wife told Sky News that she envisioned welcoming Obama and his wife Michelle to Damascus.
"I can see myself hosting them in Damascus in the old town, meeting with people, getting a sense of how we live, who we are and what Syria's about," she said.
She expressed her hop that her husband and the US president would find a common denominator due to the fact that they are both young leaders who want to make a change.
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."