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."
The Cuban government's claims estimates date to 2015 (see report, in Spanish). Since the U.S. embargo remains in place, the damage estimates could rise.
A reporter for ABC News asked the senior official how the claims between the countries could be settled with the embargo still enforced. The official replied:
"I don't think we're in a position to address that kind of a question at this point."
Trying to say how the embargo would figure into the claims discussions is "very premature," the official said.
Asked if the U.S. government had handled any claims cases with such high dollar amounts, the official said, "I don't know that there's anything exactly comparable....this is kind of a unique situation..."
Asked if Cuban officials seemed inclined to "make a real settlement," the official said, "We certainly have not heard anything that there is an unwillingness to settle claims."
U.S. officials have "provided some ideas to the Cuban government" that could lead to a settlement, but have not gotten a response.
"They have indicated that they will get back to us. We're again at the very early stages of this."