* Ghoga says resigning to stop "atmosphere of hatred"
* Protesters stormed government office in Benghazi
* NTC chief warns Libya risks entering "bottomless pit"
* Appeals for more patience with new government (Edits throughout, adds new quotes)
BENGHAZI, Libya, Jan 22 (Reuters) - The deputy head of Libya's ruling National Transitional Council (NTC) said on Sunday he was resigning after a series of protests against the new government which the country's leader warned could drag Libya into a "bottomless pit".
The protests have pitched the NTC into its deepest crisis since Muammar Gaddafi was overthrown with help from NATO powers last year, and they raise new questions about the council's ability to govern the oil exporting country.
Late on Saturday, a crowd demanding the government's resignation forced their way into the NTC's local headquarters in Benghazi while the NTC chief was inside, in the most serious show of anger at the authorities since Gaddafi's ouster.
The NTC has the support of Western powers, but it is unelected, has been slow to restore basic public services, and some Libyans say too many of its members are tarnished by ties to Gaddafi.
Abdel Hafiz Ghoga, vice-president of the NTC and one of the council's highest-profile members, was the target of some of the protesters' criticism. Last week, students jostled him when he visited a university in Benghazi and he had to be pulled to safety.
"My resignation is for the benefit of the nation and is required at this stage," Ghoga told Al Jazeera television.
He said the national consensus that helped the country rise up and end Gaddafi's 42-year rule had not lasted into peace-time, giving way to what he called an atmosphere of hatred.
"I do not want this atmosphere to continue and negatively affect the National Transitional Council and its performance," said Ghoga, who also acted as the NTC's spokesman.
Protesters say the NTC has failed to live up to the aspirations of the revolt against Gaddafi, the most violent of the "Arab Spring" uprisings.
"We hoped for security, peace and transparency. We have seen the opposite," said Miftah Al-Rabia, 28, who was standing outside the NTC's Benghazi headquarters on Sunday with a group of protesters.
NTC chief Mustafa Abdel Jalil, speaking at a news conference in Benghazi just over an hour before Ghoga announced he was resigning, appealed to the protesters to be more patient.
"We are going through a political movement that can take the country to a bottomless pit," he said. "There is something behind these protests that is not for the good of the country."
"The people have not given the government enough time and the government does not have enough money. Maybe there are delays, but the government has only been working for two months. Give them a chance, at least two months."
He said he had accepted the resignation of Benghazi's mayor, Saleh El-Ghazal, following the protests, and promised elections to choose the mayor's successor.
In a glimpse of the lack of coordination which Western diplomats say pervades the workings of the NTC, Abdel Jalil was asked if Ghoga would be stepping down and said he would not.
Sources in the NTC, who spoke on condition of anonymity, said Ghoga has not submitted a letter of resignation.
They said he was angry at being manhandled at the university and that a delegation had gone to his home to try to talk him out of resigning.
The location of the protests is particularly galling for the NTC. Benghazi, in eastern Libya, was the birthplace of the revolt against Gaddafi's rule and the site of the NTC's headquarters during the revolt.
The protests add to the list of challenges facing the NTC.
It is struggling to bring to heel dozens of armed militias who have carved the country into rival fiefdoms and are so far refusing to join a newly created national army.
Foreign states are worried about the NTC's capacity to secure its borders against arms traffickers, al Qaeda insurgents and migrants trying to reach Europe illegally.
The NTC was formed in the early days of the revolt against Gaddafi from a hastily-assembled group of lawyers, government officials who defected, Muslim clerics, tribal leaders and civil society activists.
At the time, Gaddafi's troops were using automatic weapons to fire on protests in Benghazi and elsewhere, and there was little time to vet the members.
But nearly six months on from the moment the rebellion took control of the capital Tripoli, Libyans are started to question the council's legitimacy.
In particular, some people have cast doubt over the loyalties of former Gaddafi lieutenants who are now in the NTC. These include Abdel Jalil himself, who was justice minister under Gaddafi before defecting early in the uprising.
The council says it will dissolve itself once elections are held for a transitional national assembly. That vote is scheduled to take place in about six months.
At the NTC headquarters in Benghazi on Sunday, smashed windows bore witness to the protests on Saturday night. Guards in camouflage fatigues patrolled the building.
"We still don't know who exactly is in the NTC. There is no transparency," said Al-Rabia, a protester standing outside the building with a group of about 30 other men.
Another protester, 24-year-old Mohammed Mahmoud, said he fought against Gaddafi during the revolt and wounded his shoulder and hand.
"We fought on the front line and received injuries but we did not see the NTC with us," he said. "I have one single question: Why has the NTC failed at everything except selling oil? We want to correct the path of the revolution." (Additional reporting by Omar Fahmy in Cairo, Ali Shuaib and Taha Zargoun in Tripoli and Mohammad Al Tommy in Benghazi; Writing by Christian Lowe; Editing by Elizabeth Piper)