Police spokesman Ezzedine al-Fazani said that the attack was linked to the recent detention of a man allegedly involved in last month's assassination of the head of one of the city's security agencies, National Security chief Col. Farag el-Dersi.
The unknown assailants attacked the security compound, in an apparent attempt to break into a nearby detention center where the suspect in el-Dersi's killing is being held.
In Benghazi, where the revolt that unseated longtime ruler Moammar Gadhafi began last year, security has sharply deteriorated over the past year. An attack in September on the U.S. Consulate in Benghazi killed U.S. ambassador to Libya Chris Stevens and three other Americans.
Security in the country's south is also of concern.
Libya's parliament on Sunday voted to close the country's borders with Sudan, Niger and Chad, declaring the south a restricted military area.
The decision affects cities such as Kufra and Sabha, which have been the scene of armed clashes this year that have left more than 100 dead. The fighting has been mainly between the African tribe of Tabu and their rivals, the Arab tribe of Zwia.
General National Congress spokesman Omar Humidan says the parliament voted to seal Libya's southern borders with its African neighbors to stem the flow of illegal immigration and population changes.
The African Tabu, the original inhabitants of south Libya, were heavily suppressed under the Gadhafi regime. They accuse the new government of continued discrimination.
The GNC did not specify how long border crossings would be sealed or how Libya's military plans to secure the long and porous border. The military does not have a strong presence along the southern border and is struggling to rebuild itself - relying heavily on former rebels as part of its force - after last year's civil war that ousted Gadhafi.
A military official, who wished to remain anonymous because he was not authorized to speak to reporters, said the government's main concern is not the influx of people, but the illegal flow of weapons.
A flood of weapons, including explosive warheads and small arms ammunition, have been smuggled from Libya to Egypt since the outbreak of revolutions in both countries last year. The weapons have fallen into the hands of Islamist militants in the Sinai Peninsula, or pass through smuggling tunnels to the Palestinian Gaza Strip.
The U.S. State Department said last week that it provided funding to U.S. Customs and Border Protection to conduct training last week in McAllen, Texas for 13 officials from the Libyan Ministry of Defense and the Customs Authority.
The State Department statement said the program specifically focuses on reducing the illicit transfers of weapons across borders. It is the third course undertaken by the State Department and Homeland Security with the Libyan government to improve border security.
(Copyright 2012 by The Associated Press. All Rights Reserved.)