Gunmen in Libya shot dead a Swiss national working for the International Committee of the Red Cross, fired a grenade at the prime minister's office and tried to kill a renegade general in a series of attacks on Wednesday.

The violence, which underscores the almost total lack of security in the North African state, followed an overnight rocket attack on the government's offices in the capital, Tripoli.

In Geneva, the International Committee of the Red Cross confirmed that one its workers, Michael Greub, 42, was killed by gunmen in the city of Sirte.

Greub, who headed the agency's office in Misrata, 200 km from Sirte, was leaving a meeting with two colleagues when the attackers shot at their vehicle at point-blank range, said ICRC spokesman Wolde Saugeron.

The other two staff members were unharmed.

"The ICRC vigorously condemns this heinous attack," said Director-General Yves Daccord, deploring the loss of "a devoted humanitarian who spent many years of his life helping others".

Anarchy is spreading in the oil-producing nation where turmoil and political infighting have reigned since the 2011 unrest that ousted Muammar Gadhafi. Many armed militias operate at will beyond state authority.

In the east outside Benghazi, ex-general Khalifa Haftar survived an assassination attempt. In Tripoli, gunmen fired a rocket-propelled grenade at the office of Prime Minister Ahmed Maiteeq.

Nobody was hurt when the grenade hit the kitchen on the same floor as Maiteeq's office, an aide said, adding that the premier was not there at the time.

Maiteeq was elected by parliament last month in a chaotic vote that many lawmakers disputed. Outgoing premier Abdullah al-Thinni has refused to hand over power, saying he wants to wait for a legal ruling on whether Maiteeq's election was legitimate.

In an attempt to reinforce his authority, Maiteeq took over the premier's office on Monday night, backed by a police escort.

Hours before the attack there, a suicide bomber blew up a sports utility vehicle packed with explosives at Haftar's base in Benghazi, his spokesman Mohamed El-Hejazi and army officials said.

Haftar survived but four men from his force were killed and 23 others slightly wounded, a medical source said.

Speaking later on television, Haftar said he had been treated for minor wounds at a hospital. "I am well. There will be a strong response," he said, without elaborating.

His campaign to rid Libya of Islamists has triggered heavy fighting in Benghazi in the past few weeks, killing dozens of people.

Gadhafi's one-man rule and years of unrest since have left Libya with few functioning institutions and no credible army to impose state authority on former fighters and Islamist militants who often use military muscle to make demands on the state.