Al-Assad also spoke of "the necessity to remove obstacles that hinder relations and to promote stability in the Middle East".
US-Syrian relations have deteriorated following the US invasion of Iraq in 2003 and the assassination of Rafiq al-Hariri, the former Lebanese prime minister, in 2005, which many blame on Syria. Damascus denies such allegations.
The US withdrew its ambassador to Syria after al-Hariri's murder.
However, Obama has encouraged good relations with Damascus, with Jeffery Feltman, Washington's foremost Middle East envoy, visiting the country in March.
Feltman's visit was the first high-level US trip in four years.