The incidents highlighted the turmoil in Libya where the government is trying to restore order in the oil producing country, which is awash with weapons after the 2011 ouster of former dictator Muammar Gaddafi.
The blast in Brak al-Chati, near the main southern city of Sabha, happened on Thursday after a group of 43 locals and Africans were entering the army depot to steal ammunition, a security official said.
The casualties could rise further as the depot was still on fire and people might be trapped inside, the official said.
Libya's nascent military is struggling to secure army bases and curb extremist militants, militias and gangs who fought in the uprising against Gaddafi but refuse to disarm and control parts of the country.
The four soldiers were killed in Benghazi as clashes erupted between army special forces and Salafi militants of the Ansar al-Sharia group, officials said.
The trouble started when soldiers stopped a car loaded with weapons, explosives and large amount of money. "Three soldiers were killed in clashes with Ansar al-Sharia," Wanis Bukhmada, commander of the special forces in Benghazi, told a news conference.
He later told Reuters: "We will defend Benghazi."
Another soldier was assassinated by unknown gunmen in the morning in another part of the city, a security source said.
Fighting had initially started on Monday between army special forces and members of the Ansar Sharia in Benghazi, Libya's second-largest city. At least nine people were killed before the militants retreated from their main base. Three more soldiers were killed on Wednesday.
Army officials went on nationwide television on Thursday to appeal to the militias to lay down their weapons in Benghazi and start a dialogue.
"Brothers of the Ansar al-Sharia. You are Muslims and we are Muslims. We don't differ on religion ... but don't impose something which is not part of the religion," Salah Obeidi, army commander of the eastern region, told reporters.
The security situation has sharply deteriorated in the past few months in Benghazi, where car bombings and assassinations are part of daily life.
Most countries have closed their consulates in the city of one million inhabitants, home to several oil companies. Some foreign airlines also have stopped flying there.
Ansar al-Sharia was blamed for the attack on the US consulate in Benghazi in September last year when the US ambassador and three other Americans were killed.
BA/BA