An American teacher was gunned down in Libya as he took his morning jog Thursday, a week before he was to return home on holiday, officials and the school said.

Ronnie Smith, a 33-year-old from Texas, had been running in the central Al-Fwihet neighbourhood of the eastern city of Benghazi when he was shot, security services spokesman Ibrahim al-Sharaa said.

No one has yet claimed responsibility for the killing, which comes 15 months after the US ambassador and three other Americans were killed in an attack on the US consulate in Libya's second city.

International School Benghazi director Adel al-Mansuri said Smith, who was married and the father of a two-year-old boy, had joined the faculty as a chemistry teacher late last year.

Mansuri said Smith had been set to return home next week for the year-end holidays, but it was not immediately clear whether his wife and son were with him.

The director added, without providing details, that another American teacher at the school had been taken to a secure location until he can travel home.

The State Department confirmed that a US citizen had been shot and killed in Benghazi.

"We offer our condolences to the victim's loved ones. We are in contact with the family and are providing all appropriate consular assistance," deputy spokesperson Marie Harf said.

Smith's killing triggered an outpouring of emotion on social media networks.

"It is with a very heavy heart that we announce the death of Ronnie Smith... shot & killed in #Benghazi," tweeted the Libyan Youth Movement.

"Ronnie was living and teaching in #Benghazi on his own accord, he told friends 'If I were to be killed, I will die for Education.'"

Another Benghazi-based Twitter user identified as Taqwa Embasher posted: "Smith was a kindhearted, generous person. I was a target of his kindness and generosity" RIP my best teacher&friend."

International School Benghazi is one of the few foreign schools still operating in Libya, with most having shut down last year and earlier this year because of the growing lack of security.

In other violence in the increasingly lawless eastern city Thursday, two Libyan soldiers were shot dead in separate incidents, the latest of dozens of security personnel to be gunned down in recent weeks, security officials said.

A third soldier, who was attached to military intelligence, died when a bomb placed under his vehicle blew up, a security official said.

The violence rocking the city, which was the cradle of the NATO-backed rebellion that ousted Moamer Kadhafi, is largely blamed on jihadist groups that have mushroomed since the veteran was toppled and killed in 2011.

Chief among them is Ansar al-Sharia, a jihadist group accused of the September 11, 2012 attack on the US consulate that killed ambassador Chris Stevens and three other Americans.

Farther east, in the Islamist bastion of Derna, residents on Thursday staged new demonstrations against what they say is anarchy in the city and to demand a police and army presence.

On Monday, unknown gunmen fired on protesters in Derna, killing one and wounding seven, according to an updated toll given by a medic on Thursday.

Like Benghazi, Derna has seen a wave of killings of members of the security forces and the judiciary in attacks blamed on Ansar al-Sharia.

The group implicitly denied responsibility for Monday's attack on protesters in Derna.

"Opening fire with live rounds on protesters... is a dangerous thing," the group said in a statement received on Thursday by AFP.

Prime Minister Ali Zeidan announced on Wednesday that preparations were under way to send troops to Derna, where law and order is almost non-existent.

Libya's new authorities have tried in vain to integrate former rebels who helped topple Kadhafi into the regular armed forces, with many militias carving out their own fiefdoms, each with its own ideology and regional allegiances.