WASHINGTON — On the same day the Pentagon announced it had killed yet another Islamic State leader that few Americans have heard of, Fawaz Muhammad Jubayr Al-Rawi, American officials also said they do not know if the Islamic State’s most well-known name, Abu Bakr al-Baghdadi, is still alive.

Officials cautioned that they have no evidence that Mr. Baghdadi is dead. But the dueling narratives illustrate the plodding nature of the Defense Department’s fight against the militant Sunni Islamic extremist group, which is, after almost three years of airstrikes, on the back foot in both Iraq and Syria.

Every couple of weeks, the United States Central Command, which oversees combat operations in the Middle East, announces the death of an Islamic State leader who has been killed in airstrikes. On Tuesday, it was Turki al-Bin’ali, whom the American-led coalition called the “self-proclaimed grand mufti or chief cleric” of the Islamic State, killed in a May 31 airstrike in Mayadin, Syria. Two weeks before that, it was Samir Idris, whom the Defense Department said was a “key” Islamic State financier of attacks around the world, also killed near Mayadin.

On Friday, it was Mr. Rawi, a Syrian labeled by the Pentagon “an experienced terrorist financial facilitator,” who moved millions of dollars for the Islamic State’s attack and logistics network.