MISRATA, Libya » Libyans have puzzled for four years over what might arrest their country’s disintegration.

Feuding factions have consistently reached for guns instead of compromises in their battle to fill the vacuum left by the fall of Moammar Gadhafi, ultimately breaking the country into two warring coalitions of militias and city-states. Leaders on both sides vowed that Libya’s only hope was their own military victory.

But now a growing number of politicians on both sides of the conflict say that the dual threats from colonies of the Islamic State and a looming collapse of the economy may finally jolt Libya out of that spiral. In a series of interviews in five Libyan cities on both sides of the fight, political leaders were for the first time trying in earnest to reverse that trend, calling for unconditional negotiations and reciprocal concessions.

"It is the realization that Libya is in danger," said Fathi Bashaagha, a businessman who leads the pro-unity faction now ascendant in the pivotal city of Misrata, whose powerful militias have been fighting in several places around the country. "Nobody can win. We have only one way we can survive, and that is a unity government."

Abubakr Buera, an influential lawmaker who last year led the Parliament to move to the side opposing Misrata, said he now agreed, "to save the misery of the people."

Their efforts give at least a glimmer of hope to United Nations-sponsored reconciliation talks now taking place in Algeria. But they still face long odds, in part because of the presence of extremists averse to any compromise and in part because of the personal ambitions and mutual distrust among leaders of both factions.

Against doves warning of an imminent catastrophe, hawks continue to minimize the threats, insisting that a military triumph is the only lasting solution.

"It will take some time, but it is possible to win the war, and the winner is going to be the winner," asserted Abdulrahman Swehli, previously the most influential political figure in Misrata and still the leader of a hawkish camp opposed to Bashaagha.

The reports about the growth of Islamic State in Libya were "propaganda," Swehli said, and the economic situation was "bad but not dire." He accused the U.N. diplomat leading the unity talks of "making things worse" by trying to isolate those like himself who still saw the domestic conflict as an existential battle.

Still, the chiefs of Misrata’s civilian and military councils both said that the majority of the city was backing Bashaagha and the unity talks, both because of fatigue with the battle and a sense of the growing dangers.

"We are not as united as we once were," Swehli conceded. "Some people are getting tired."

Each of the two coalitions now has its own rival provisional government, each riven with internal divisions.

The side that is recognized internationally, centered in the eastern cities of Tobruk and Baida, is dominated and defined by Gen. Khalifa Hifter, 72, who once fought for Gadhafi but later broke with him to join the exiled opposition. Hifter last year announced his own attempt at a military takeover, promising to purge Libya of both moderate and extremist Islamists.

Libyans fearful of the extremists have embraced him as a hero, while others have denounced him as a second Gadhafi. The western city of Zintan has allied with him mainly in shared opposition to the expanding influence of the coastal city of Misrata.

The other coalition, centered in Misrata, controls the capital, Tripoli. It includes both moderate and extremist Islamists as well as Berber tribes and much of the former exiled opposition to Gadhafi — all united mainly by a fear of Hifter.

Their battles killed more than 2,800 people last year and displaced about 400,000, according to a recent U.N. report. They have destroyed or incapacitated Libya’s two main airports, flattened districts of major cities, and disabled much of the oil and energy infrastructure. Libya, despite its oil wealth, now suffers widespread blackouts, gas lines and even shortages of cooking oil.

Both factions have continued to draw on the same central bank to meet increasingly inflated payrolls, often for no-show jobs or inflated militia budgets. Public payroll costs tripled to $24 billion in 2014 from $8 billion in the year before the uprising of 2011, said Musbah Alkari, manager of the reserves department at the Central Bank of Libya, while oil revenue plunged.

Libya could run a deficit of more than $40 billion in 2015, quickly burning through its foreign reserves of about $90 billion, according to Central Bank figures. The currency may collapse in less than two years, Alkari said, but many Libyan politicians still believe that Libya is rich and that "we can’t go broke."

Fighters pledging loyalty to the Islamic State, also known as ISIS or ISIL, control the midcoastal city of Surt and a militia in the eastern city of Derna. They have claimed responsibility for attacks on Misrata militias, a Tripoli hotel, government buildings, foreign embassies and a major oil field as well as the beheading of a group of Egyptian Christians.

The Tobruk-Bayda government’s leaders say their current war is against extremism, but a growing number of lawmakers in its Parliament now argue that a unity government is the only way to defeat it. "I hope we can all stand up and expel the terrorists together," said Muad Rafa Mosod, a 30-year-old lawmaker from the south.

Elected last year and now based in Tobruk, the Parliament confers legitimacy on the Tobruk-Bayda government and it has named Hifter its top military commander.

But it does not disclose its attendance or vote counts. In part because of a boycott by members opposed to Hifter, fewer than 110 members in the 200-seat chamber usually met last year and attendance has since fallen below 90.

In the first vote last year on the unity talks, more than 50 voted against and fewer than 50 voted in favor, several lawmakers said. But the most recent vote had flipped to 65 in favor and 12 against, according to Buera, the first speaker and an influential member.

In Tripoli, even the chief of staff overseeing his faction’s war effort said that neither side could win on the battlefield. Without a unity government, said the chief, Jedalla al-Obeida, "We will have city-states and a Somalia scenario."

But like the Misratan hawks, the military leaders in Tobruk and Bayda show no sign of relenting. In an interview, Saqr al-Jarushi, chief of Hifter’s small air force, accused the Misratans of plotting to bring Jews to Libya and praised Gadhafi for his crackdowns on Islamists. "It was better that he killed them," Jarushi said, "because otherwise they would be heads of militias just as they are now. This is what Gadhafi was afraid of."

But how to deal with genuine extremists also remains an unanswered question for the Misrata coalition. Their coalition includes Ansar al-Shariah of Benghazi, the extremist group linked to the attack that killed Ambassador J. Christopher Stevens in 2012 and widely blamed for a campaign of bombings and assassinations against security and other perceived foes.

Misrata-Tripoli leaders tend to dodge questions about their Ansar al-Shariah allies. Jamal Naji Zubia, head of the Tripoli foreign media office, recently suggested that the Benghazi Islamist fighters should address the problem by better explaining themselves through the news media. "I told them, ‘You say you are mujahedeen and you are not afraid of death, so why are you afraid to show your faces?’"

Mohamed Dayri, foreign minister of the Tobruk-Bayda government, said he told the U.N. envoys that talks were "necessary but not sufficient" to defeat the extremists. "A political track, yes, but what about a military track?" he said.

On the other side, even the most conciliatory leaders of the Misrata-Tripoli faction are dead set against any role for Hifter.

"He just wants to be on top of the throne," Bashaagha said. "We had that experience for 40 years, under Gadhafi."

Then any unity government would face the same challenge that undermined its predecessors: how to exert civilian control over the feuding militias.

"At some point, they are going to realize that you can point as many guns as you want and you still can’t pay salaries," said Motasim Elalem, 39, a banker in Tripoli. "I keep waiting for Libya to hit rock bottom," he added, "but I think we are going to have to burn it down first."

David D. Kirkpatrick, New York Times