The back-and-forth indicated the confusion in Libya's decision-making and power struggles among different groups ahead of the country's first national elections, a major landmark in the transition after the fall last year of longtime leader Moammar Gadhafi.
The election is to choose a 200-member assembly tasked with forming a new government and write a new constitution.
Both the NTC and the government of Prime Minister Abdurrahim el-Keib have faced persistent criticism that they have been ineffective in tackling the multiple troubles facing the deeply divided nation - and the two sides have traded accusations over who is to blame.
Two members of the NTC, Fathi Baja and Moussa al-Kouni, told the Associated Press on Thursday that the council had voted to remove the government during a meeting the day before. But, they said, the council did not intend to make the decision public until a replacement was decided. Baja said 56 of the council's 72 members attended and most of them supported the no-confidence motion.
"There is an agreement inside the council to oust el-Keib government," he said.
NTC spokesman al-Hareizi described the report as "baseless" in a brief statement carried on the official news agency LANA.
Al-Amin Belhaj, another NTC member and a leading member of the Muslim Brotherhood, said the council would meet on Sunday to finalize the extent of the government reshuffle, suggesting that part of the cabinet could be retained. He said a formal vote had not been held Wednesday. Another member, Ahmed al-Abbar, described the forthcoming meeting on Sunday as "decisive."
A witness who attended Wednesday's meeting said that members made a show of hands that reflected a strong majority calling for removing the government. But there were sharp divisions over who would replace Keib, said the witness, who spoke on condition of anonymity because of the sensitivity of the subject.
Islamists in the council support Mustafa Abu-Shakour, Keib's deputy. Others oppose appointing a senior member of a cabinet they say has failed, suggesting Labor Minister Mustafa al-Rajbani instead, according to Baja.