The department said in a press release: "Of these seven Swiss nationals, some have already left the country, and others will follow in the next few days."
However, two other Swiss citizens will "still be unable to leave the country," and the work of Swiss companies operating in Libya will not be able to return to normal, the statement said.
The department will continue its "persistent efforts to find a solution to the problems that continue to burden relations between Switzerland and Libya."
The diplomatic row between Libya and Switzerland was sparked by the July 15 arrest in Geneva of Muammar Qaddafi's son Hannibal, after staff at the five-star hotel he was staying at with his wife alerted police that the couple had been beating two servants who were part of their entourage.
Hannibal spent two days in custody, while his pregnant wife Aline was under police supervision in a clinic in Geneva. They were released on $490,000 bail two days later and left Geneva.
Libya, an OPEC member, halted oil deliveries to Switzerland and arrested two Swiss citizens in an apparent retaliation. The Libyan embassy stopped processing visa requests from Swiss nationals, and Swiss firms were forced to close their Libyan branches.
However, Libya later resumed oil supplies to Switzerland and also released on bail two Swiss nationals, who are currently at the country's embassy in Tripoli but have not yet been given permission to leave Libya.
