A pre-dawn attack on the the office of the International Committee of the Red Cross in the western Libyan city of Misrata wounded one person, the organisation's spokeswoman said on Tuesday.
"We do not know if the office was hit by a shoulder mounted rocket or a bomb placed next to the building," Sumaya Beltaifa told AFP.
She said the blast wounded a Libyan citizen who lives next to the offices and caused serious material damage to the ICRC building.
No one was wounded from a crew of 30 ICRC workers, she added.
Beltaifa stressed that ICRC activities are "strictly humanitarian" and "have no relation with religion or politics."
This is the second such attack on the organisation in less than a month.
On May 22, a rocket-propelled grenade struck ICRC offices in the eastern city of Benghazi, cradle of the revolt that toppled Moamer Kadhafi last year.
The Brigades of the Imprisoned Sheikh Omar Abdul Rahman claimed responsibility for that first attack on the ICRC in an online statement.
The same group, according to SITE monitoring services, is linked to last week's bombing of the US mission in Benghazi in which one person was wounded.
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It said it was avenging the death of Al-Qaeda number two Abu Yahya al-Libi in a drone strike in Pakistan, said the US-based SITE, which monitors jihadi websites.
Libi was a Libyan national and is said to have sympathisers in his homeland.
The Brigades also said the June 6 bomb attack at the US diplomatic mission -- in which one person was wounded -- had come in response to the use of "American drones flying in Libyan skies," SITE said.
The group is named after Abdel Rahman, 73, who received a life sentence in the United States for his involvement in plots to hit New York targets and a plan to assassinate former Egyptian president Hosni Mubarak.
Abdel Rahman, known as the "Blind Sheikh," is also cited as one of the inspirations for the first attack on the World Trade Center, which killed six people and injured more than 1,000 in 1993.
The latest attack on the ICRC comes one day after a rocket-propelled grenade hit a British diplomatic convoy, wounding two security guards.
Even though such violence has become increasingly common, Libyan authorities insist they are carried out by "isolated individuals" rather than "organised extremist groups.""
Libya is awash with all kinds of weapons after the fall of Kadhafi's regime.
The wave of unrest comes as the North African nation prepares to elect a general national congress, with the vote set for July 7.