Libya's premier was due to meet local authorities in Benghazi on Sunday, a government source said, as special forces units patrolled the city a day after clashes with gunmen killed six soldiers.

Prime Minister Ali Zeidan was due to travel to the eastern city with members of his government to discuss the security situation, the source said on condition of anonymity.

An onlooker in Benghazi told AFP that "special forces soldiers have been deployed in the city and patrolled the streets, which are calm again".

Amid the trouble and its aftermath, Libya's highest political authority, the General National Congress, postponed a vote to choose a replacement for its head, Mohamed al-Megaryef.

Megaryef resigned on May 28 after the GNC adopted a law banning officials who had served under ousted dictator Moamer Kadhafi from government jobs.

Elsewhere in Libya, gunmen shot dead an appeal court judge in the eastern town of Derna on Sunday, official news agency LANA cited the head of the court, Abdelaziz Trabelsi, as saying.

"Judge Mohammed Ibrahim Houidi, president of the criminal division, was killed on Sunday morning as he left the appeals court building in Derna," he said.

Trabelsi added that the attackers had fled immediately after the shooting, quoting witnesses.

Eastern Libya has been the scene of attacks targeting judges, soldiers and policemen who served under Kadhafi's regime.

A senior US official visiting Algeria on Sunday said Washington was committed to supporting Libya in the transitional period after its revolution.

"We must all support the Libyan government as they try to move forward to the destiny the Libyan people have asked for for themselves," Under Secretary of State for Political Affairs Wendy Sherman told a news conference.

She said she had talked to Algerian officials about how Algiers could improve the situation in neighbouring Libya.

"Algeria is a leader in the region... and I think if we all work together we can help the Libyans succeed," she said.

Late on Saturday, Libya's grand mufti Sheikh Sadeq al-Ghariani called for residents of Benghazi to "stay calm" and unite during "this difficult phase that the country is passing through".

In a television appeal, Ghariani also urged the "General National Congress to open an investigation and put an end to this spiral of violence".

The head of the security forces' joint operations room, General Mohammed Sherif, said that "special forces have identified the attackers... and some of them have been arrested," without giving further details.

Clashes between elite forces and gunmen killed six soldiers and wounded five in Benghazi on Saturday, the military said.

Benghazi, the cradle of the uprising that ousted Kadhafi's regime in 2011, has been increasingly rattled by attacks on security forces and Western interests, often blamed on Islamists.