The US cut diplomatic relations with Syria after the 2005 assassination of Rafiq al-Hariri, the former Lebanese prime minister. Syria denies involvement.
But Obama, who took office in January, has introduced a new approach to the Middle East and offered dialogue with states such as Syria and Iran.
Earlier this month, John Kerry, the head of the US senate foreign relations committee, visited Syria as part of a congressional delegation.
Kerry said he saw possibilities for "real co-operation" between Washington and Damascus.
He said he was also encouraged by his "very long, candid, open" discussion with Bashar al-Assad, Syria's president, and said he sees the possibility of progress ahead.
"While we will disagree on some issues for sure, what I heard and what I will take back with me and, hopefully, what we could put in place to take advantage of it, is the possibility of real co-operation on a number of different issues beginning immediately, beginning soon," Kerry said.
The meeting between Moustapha and Feltman comes a day after the state department released its annual survey on global human rights violations.
The survey said the Syrian government continued to commit serious abuses and said its respect for human rights had worsened.
"Security forces arbitrarily detained and tortured detainees and the government imposed significant restrictions on freedom of speech, press and assembly amid an atmosphere of government corruption," it said.
"In a climate of impunity, there were instances of arbitrary or unlawful deprivation of life."
There was no immediate comment on the survey from Syria.