Representative Saleh Jaauda, an independent from the second city Benghazi, told AFP that the government team failed to win the assembly's approval because "it did not meet the aspirations of the Libyan people."
Abu Shagur made a televised statement shortly after the vote, saying he had picked "highly-qualified" individuals for his cabinet and that he had expected the congress to discuss the merits of each individual candidate.
"Knowing the objections would help me offer (better) alternatives," he added, stressing that he had picked his cabinet on the basis of competence, experience, courage and geographical considerations.
Abu Shagur said he formally asked the assembly to withdraw and amend the list. General National Congress representatives had began discussing the lineup late Thursday after more than 100 demonstrators had barged into their headquarters complaining that the western town of Zawiyah was not represented on the list.
Several representatives criticised the proposed cabinet during an extraordinary meeting which was broadcast live on television.
"Abu Shagur did not deliver the government he promised -- it is neither a government of national unity nor a government representative of all the regions," said one representative.
"We didn't receive their CVs," complained another, stressing this showed a lack of respect for the legislative assembly.
"Most of the ministers presented on the list were in the previous government, are incompetent or unknown," added a third, who like the others was not named in the broadcast.
Abu Shagur's proposed government would have kept several minister from the previous cabinet, which was widely criticised for its failure to take tough stances on security and plagued by corruption scandals.
The suggested cabinet also left out the National Forces Alliance, a liberal coalition under the leadership of war-time prime minister Mahmud Jibril, which proved to be the most popular party in July elections.
On Wednesday, the liberal coalition issued a statement saying it gave its support to Abu Shagur although it would not take part in the government, in the wake of failed negotiations.
The Justice and Construction Party, which was spawned by the Muslim Brotherhood and is the second largest, expressed its disappointment over the cabinet earlier on Thursday.
This is not "the national consensus we were aiming for in order to get the country out of its current crisis... Nor is it a predominantly technocratic government," said the party in an online statement.
The support of the Justice and Construction Party and its allies helped Abu Shagur win his post in September by giving him a small margin over Jibril, who had won the first round.
Mohammed Megaryef, president of the GNC, announced in the middle of the heated debates that Abu Shagur had called him requesting to withdraw his list and present an alternative one.
The representatives were supposed to vote on each minister one by one on Thursday but instead they decided to extend Abu Shagur a chance to present an alternative lineup by October 7.