The two sides had "substantive" discussions on Thursday in Washington, D.C., and agreed to meet again in Havana to resume conversions over ways to reach a mutually acceptable agreement, the official said in a background discussion with reporters.
Cuba claims that the U.S. embargo has caused $181 billion in "human damages" and $121 billion in economic harm.
The U.S. government contends that Cuba must settle $1.9 billion in property claims - plus 6 percent interest - in property claims dating from the late 1950s and 1960s; $2.2 billion in court judgments; and hundreds of billions of dollars in mining claims.
The senior official said it was premature to try to predict how long it would take the two countries to settle their claims, but said Cuban officials seemed to be taking negotiations seriously.
U.S. officials have stated their "desire to resolve claims as quickly as possible," the senior official said.
No date has been set for the next round of discussions.
"Both sides agreed we'd have more regular meetings," the official said. "We would expect to go to Havana for the next meeting."