The British Foreign and Commonwealth Office said at least 30 people were reported dead following clashes between rival tribes in Sabha, a southern Libyan city.
Libyan Deputy Interior Minister Hassan al-Drowi was assassinated during the weekend in Sirte, a city east of the capital Tripoli.
"The U.K. is committed to supporting the Libyan authorities as they continue their efforts to build a more stable and secure Libya," British Minister Hugh Robertson said in a statement.
The BBC reports Drowi's assassination is the first such slaying of a member of the transitional government.
The British government was one of the first to recognize a government that emerged when the regime of Moammar Gadhafi collapsed in late 2011. Gadhafi died after falling into rebel hands in Sirte during the waning stages of the 2011 conflict.
Libya has struggled to establish a sense of national security since the end of fighting in 2011. Rival claims to autonomy in parts of Libya have pitted pro- and anti-government forces against each other.
The independent Libya Herald reported Tuesday members of the General National Congress were fired on during a session in Tripoli by unknown gunmen. The report said GNC members were discussing a no-confidence vote against Prime Minister Ali Zeidan at the time of the incident.
No injuries were reported.