Their National Amazigh Congress called on all Libyans, and Berbers in particular, to end cooperation with the National Transitional Council and with the interim government.
Kib had insisted as he announced the names of ministers that the new cabinet would be inclusive and representative of all of Libya's far-flung regions.
"I can reassure everyone: all of Libya is in the new government," the interim prime minister told reporters in the capital.
But in Benghazi, Libya's second-largest city and the rebels' wartime base, several dozen protesters marched against the new government, charging that the cradle of the revolution was unduly under-represented.
Representatives of the Toubou minority in the Saharan southwest, who fought a bloody desert war against Kadhafi's forces, also protested that their role had not been given adequate acknowledgement.
Some heroes of the rebellion were given key posts after the thwars -- the armed civilian brigades that have yet to lay down their weapons -- put pressure on Kib.
The interior ministry went to Fawzi Abdelali from Misrata, Libya's third-largest city, which withstood a devastating six-week siege by Kadhafi forces and whose fighters captured and killed the fallen despot in October.
The defence ministry went to Osama Juili, commander of the fighters who seized Kadhafi's most prominent son Seif al-Islam last Saturday after three months on the run.
Juili commands fighters from Zintan, a hilltown in the Nafusa, but his appointment failed to satisfy the aspirations of the region's Berber community as he himself is an Arab.
Bringing in an older generation of opposition figures into what he billed a government of technocrats, Kib chose Ashur bin Khayyal, Libya's envoy to Canada under the Kadhafi regime who joined the opposition in the 1990s, to head the foreign ministry.
Abdelrahman bin Yazza -- a former official in Italy's energy major ENI -- was named interim oil and gas minister.
US Secretary of State Hillary Clinton welcomed the new cabinet and vowed that Washington would work closely with it.
"The formation of a new cabinet by the (National Transitional Council) is a significant step in Libya's transition to a true democracy that is inclusive and representative of all Libyans," she said in a statement.
Clinton said the United States would work with "the new interim government to address the key challenges that remain, such as protecting and respecting the rights of all Libyans."
In a reference to the thwars, she highlighted the need to consolidate "control over militias" as well as "ensuring a functioning and credible government and preparing for the transition to an elected government."
Neighbouring Tunisia also welcomed the new government, with a foreign ministry statement underlining "the strong willingness of Tunisia to consolidate cooperation with Libya and to work with members of the Libyan government for a strategic partnership."