“Several senior U.S. administration officials” have told CNN that an Islamic State capture of Kobane, the Kurdish center in northern Syria, is not a major concern.

The officials said Washington’s primary goals are not to save Syrian cities and towns, but to go after the Islamic State’s senior leadership, oil refineries, and other infrastructure. This would limit the “sanctuary” for Islamic State forces, supporting their offensives in Iraq.

The American goal is to repel the jihadists in Iraq first and then eliminate some of its leadership and resources in Syria, the officials said. By that time, some Syrian insurgents will have enough training to confront the Islamic State.

The comments cut against the declaration by General Martin Dempsey, the Chairman of the Chiefs of Staff, in a Tuesday interview with ABC News, “I am fearful that Kobane will fall.”

More ABC news videos | ABC Entertainment News

The officials said the US would like Turkey to do more about the Islamic State’s battle for Kobane, urging Ankara to fire artillery at jihadist targets across the border.

However, the officials said the Erdoğan Government is reluctant to intervene because of the complicated relationship with Turkish Kurds.

See Turkey Feature: 14 Killed in Kurdish Protests Over Syrian Town of Kobane

A US official said — apparently unaware of the comments of his colleagues about the lack of American concern — “This isn’t how a NATO ally acts while hell is unfolding a stone’s throw from their border,” said the official.

Sources said Secretary of State John Kerry had multiple phone calls in the last 72 hours with Turkish Prime Minister Ahmet Davutoglu and Foreign Minister Mevlut Cavusoglu.