SIRTE, Libya » The Islamic State has established more than a foothold in this Mediterranean port. Its fighters dominate the city center so thoroughly that a Libyan brigade sent to dislodge the group remains camped on the outskirts, visibly afraid to enter and allowing the extremists to come and go as they please.

"We are going to allow them to slip out, because the less people we have to fight, the better," said Mohamed Omar el-Hassan, a 28-year-old former crane operator who leads the brigade from a prefabricated shed on a highway ringing the city.

"Why make the city suffer?" he said, trying to explain his delay.

His reluctance, more than 20 days after his brigade reached the city, is symptomatic of the crisis that has engulfed Libya since the overthrow of Moammar Gadhafi nearly four years ago.

The country has become so entangled in internal conflicts over money and power that it has all but invited the Islamic State to expand into its oil-rich deserts and coastline, offering new frontiers to the group as it comes under increasing pressure from U.S.-led airstrikes on its original strongholds in Iraq and Syria.

At least one group of fighters from each of Libya’s three regions has joined a wave of militant forces in Afghanistan, Algeria, Egypt and Nigeria that have publicly linked themselves with the Islamic State and its brutality.

But while many of those affiliations may primarily be attempts by local extremists to capitalize on the Islamic State’s fearsome name, the contingent in Sirte stands apart. In addition to dominating a city of more than 120,000 residents, the Islamic State militants here have demonstrated clear coordination with the original group based in Syria.

A recent video depicting the beheadings of Egyptian Christians kidnapped from Sirte appeared to have been taped on the Libyan shoreline, but it also featured the parent group’s signature audiovisual sophistication, orange jumpsuits and ceremonial knives. It was publicized in the main group’s online magazine then released under its media logo.

But even after the international uproar over the video, no Libyan authority has been able to take any effective action against the group. Two warring coalitions of militias have divided the country, and each — including the one that sent Hassan and his fighters, known as Brigade 166 — appears more intent on fighting the other than on thwarting the Islamic State. What is more, the battles crippled Libya’s oil exports so severely that there is now a risk that the country’s currency and economy will soon collapse.

"A currency collapse is less than two years away," Musbah AlKari, manager of the reserves department at the Central Bank of Libya, said in an interview at the bank’s headquarters in Tripoli.

Western governments are keeping a watchful eye. Fighters with Hassan’s brigade at the edge of Sirte pointed to what appeared to be a white surveillance drone or airplane circling overhead — a daily visitor, they said.

His fighters used extreme caution when circling the city. Escorting a Western journalist on a brief visit, they were careful not to enter the city itself. To reach one point on the outskirts, Hassan brought a half-dozen trucks for protection, some mounted with artillery, and his fighters kept their guns elevated on constant alert.

His brigade had established control of the airport, Hassan said. But there were no signs that they had set up checkpoints, even at critical spots like the coastal road entering the city or the main road to the airport. "See the jihad," read graffiti on a wall along the main road outside the city.

The Islamic State controls the local radio station; during the recent visit, all four stations on the dial were transmitting Islamic sermons. "They use the radio stations to broadcast, and they are attracting a lot of people to join them," Hassan said wearily.

He and other local militia leaders, citing informants inside Sirte, said they believed that the Islamic State fighters in the city numbered about 200 or less, while Hassan’s brigade can command hundreds. He insisted he needed no reinforcements. But the Islamic State fighters were deeply entrenched and stronger than expected, Hassan said.

"We came here with orders to go in and take over the city, but we were surprised by the numbers that joined them," he said.

Since arriving, his brigade had found time to apprehend some foreign workers without visas trying to move through the area, Hassan said.

But militants suspected of links to the Islamic State had nonetheless carried out several successful attacks on nonoperational oil fields south of the city, reportedly killing several Libyan guards and abducting nine foreigners. No one has claimed responsibility for those attacks.

The rival militia coalition, based in the eastern cities of Tobruk and Bayda and under the loose command of Gen. Khalifa Hifter, describes itself as fighting to rescue Libya from Islamic extremists, including the Islamic State fighters. "Libya was becoming the funding house, and they were going to export terrorism around the world," said Saqr al-Jaroushi, the air force chief under Hifter.

But the coalition’s leaders often characterize all of its opponents as extremists, including regional militias like Hassan’s. Brigade 166 fighters displayed some evidence that Hifter’s coalition had been bombing their positions outside the city, even though in this case Hassan’s brigade is on a mission against the same extremists.

In a pasture near the coast, the brigade fighters showed a journalist an unexploded cluster bomb, identified from photographs as a Soviet-made RBK series, near one of their positions. Similar munitions had evidently exploded nearby in recent days and left fragments of shrapnel in cup-size holes blasted into the dirt. Such weapons are banned under international law because of their indiscriminate nature.

Frederic Wehrey, a researcher for the Carnegie Endowment for International Peace, has said he saw evidence that Hifter’s planes had dropped cluster bombs on a bank and other civilian targets during fighting in the coastal town of Bin Jawad as well.

The coalition that sent Hassan, which is known as Libya Dawn and opposes Hifter, includes some Islamic extremist groups in the eastern cities of Benghazi, Derna and possibly elsewhere. Its supporters often try to argue that the Islamic State fighters in Sirte are merely a front for Gadhafi loyalists or supporters of Hifter.

"A lot of people who have joined this group we call the Islamic State are actually remnants of the previous regime we fought in 2011," Omar al-Hassi, prime minister of a provisional government set up by the Libya Dawn coalition in Tripoli, said in an interview here. Hassi dismissed the images of beheadings in Sirte as "a fabricated Hollywood-like video" concocted to stir trouble with Egypt.

Like many in his coalition, he mentioned a television interview with an influential Gadhafi cousin outside Libya, Ahmed Qaddaf al-Dam, who at times applauded the Islamic State from an Arab nationalist perspective for seeking to erase the border between Syria and Iraq. But Dam also denounced the group’s medieval Islamist ideology, saying it "shows the psychological state they are in and that they need mental health treatment."

Sirte, near Gadhafi’s birthplace, was the site of his last stand in 2011, when rebels from the city of Misrata joined a battle that destroyed much of the city. They ultimately captured Gadhafi and killed him after he had been taken into custody.

Hassan of Brigade 166, which comes primarily from Misrata, said that history was one reason that his forces hesitated to move in. He said he feared that aggressive military action against the Islamic State could increase its support from local tribes who still resent Misrata’s militias for the destruction of their city in 2011.

"If we went in with both guns blazing, we would have a backlash," Hassan said.

He and other militia leaders also acknowledged, though, that the core of the Islamic State in Sirte was from Misrata — a connection that could test the loyalties of other Misratan militiamen, who are typically reluctant to fight against their neighbors or cousins.

After Misratan brigades moved into Sirte in 2011, Hassan and others acknowledged, some continued to occupy the city and eventually turned into an extremist group, Ansar al-Shariah of Sirte, a parallel to organizations of the same name in Benghazi and Derna.

More than two months ago, Hassan and others said, Ansar al-Shariah of Sirte split up in a dispute over pledging allegiance to the Islamic State, and those who chose to ally with it emerged as the dominant faction. "They are the nucleus," Hassan said.

"You can say that the leaders are from Misrata," Hassan said, although he insisted that would not deter his brigade. "I am not here as a Misratan."

A fighter named Suliman Ali Mousa, 58, raised the theory that the Islamic State had become merely a "banner" for criminals or Gadhafi loyalists.

But Hassan said that hardly mattered. "If they are raising the black flag of the Islamic State and preaching Islamic State ideas," he said, "then they are the Islamic State."