Militants loyal to the Islamic State claimed responsibility Wednesday for a complex attack on a hotel in Libya’s capital, signaling an expansion of the jihadist group’s reach in the chaotic North African state while raising questions about the extent of coordination between leaders in Syria and Iraq.

The attack on the Corinthia hotel Tuesday, in which gunmen burst into the lobby and set off a car bomb in the parking lot, left 10 dead, including an American and four other foreigners. An affiliate of the Islamic State claimed responsibility for the attack and released photos of two suicide bombers it said took part.

Libya is increasingly taking on the appearance of a failed state, with its elected government forced to reside in the far eastern part of the country while a loose alliance of militias has set up a rival government in Tripoli. Fighting rages between government forces and Islamist militias in the second-largest city, Benghazi. Hundreds of thousands have been displaced, embassies have been closed and diplomats have fled, along with hundreds of thousands of foreign laborers.

The chaos following the overthrow of longtime dictator Moammar Gaddafi in a 2011 uprising has provided fertile ground for the rise of Islamist groups, including a number that have pledged allegiance to the Islamic State, which controls a third of both Iraq and Syria and has encouraged attacks worldwide.

According to postings on jihadi Web forums, groups claiming allegiance to the Islamic State are present in at least five Libyan cities, including the two largest — Tripoli, and Benghazi in the east, the birthplace of the 2011 uprising.

Islamic State supporters divide the vast, oil-rich country of 6 million into three regions, or “wilayat”: Tripoli, Barqa or Cyrenaica in the east, and Fazzan in the south.

The east is already home to Ansar al-Shariah, an al-Qaeda-inspired group suspected of involvement in the deadly assault on the U.S. Consulate in Benghazi in 2012 that killed the ambassador and three other Americans.

But in the eastern city of Darna, an Islamic State affiliate has held public events and claimed control of the city. And other militants claiming allegiance to the group have battled Libyan troops in Benghazi, often with suicide bombers.

The Tripoli attack is the largest operation in the country to be claimed in the name of the Islamic State, but it is unclear whether the attack was planned or directed by the group’s central leadership in Iraq and Syria. The group previously claimed responsibility for an attack on the Algerian Embassy in Tripoli that wounded three guards.

In its claim of responsibility, which first appeared on jihadi forums Wednesday, the group identified the attackers as Abu Ibrahim al-Tunsi and Abu Suleiman al-Sudani, noms de guerre suggesting that the former is Tunisian and the latter Sudanese.

“The operation is not the last one on the lands of Tripoli. . . . Let the enemies of God, the crusaders and their allies await what will harm them,” the message read.

“Tripoli is of strategic importance to the Islamic State and this attack takes the country to a new level, alongside other nations in the war against terrorism,” said Mahmoud Shamma, editor of Libya’s widely circulated al-Wasat daily. “So far we hear strong condemnations, but there is a long distance between this and action.”