Hezbollah official told The Associated Press news agency the group had no immediate comment on Carter's remarks but said it might issue a statement, most likely on Wednesday.
The official spoke on condition of anonymity because he was not authorised to speak to the media.
Washington blames Hezbollah for the explosion that killed 241 US Marines at their Beirut barracks in 1983, as well as for two attacks on the US embassy in Beirut and the 1985 TWA hijacking that killed an American serviceman on board.
Hezbollah denies the accusations and says it opposes terrorism.
Carter was widely criticised in April when he met in Syria with Khaled Meshaal, the exiled Hamas political leader.
The US also labels Hamas, the Palestinian group that controls the Gaza Strip, a "terrorist" organisation.
The Mashaal-Carter meeting led to the delivery of a handwritten letter from Israeli soldier Gilad Schalit, who was captured by Hamas-linked fighters near the Gaza border in 2006, to his parents.
While in Lebanon, Carter said he will meet with Michel Suleiman, the Lebanese president and Fuad Siniora, the prime minister.
"I will also be making an assessment on whether the Carter Center will monitor the elections that we hope will be held on time next June," Carter said.
Next year's elections are expected to be fierce between US-backed groups that hold majority seats in the current parliament and those backed by Syria, including Hezbollah.