WASHINGTON--Defense Secretary Chuck Hagel on Thursday conceded that the Syrian regime "derives some benefit" from U.S. and allied airstrikes on Islamic State militants, saying it was one of the region's complexities.

Still, Hagel said, the U.S. was pursuing a long-term strategy to stabilize the region.

Key U.S. allies, including Turkey and France, repeatedly have expressed concern the U.S. lacks a clear strategy for Syria, and that airstrikes against Islamic State risk enhancing the Assad regime's hold on power, rather than weakening it.

Privately, Mr. Hagel has raised his own concerns about the U.S. approach to Syria, defense officials said. Mr. Hagel in a memo to White House national security adviser Susan Rice said last week that the U.S. should clarify its approach to Syrian President Bashar al-Assad, officials said.

The defense chief, the officials said, is concerned about keeping together the coalition assembled by the U.S. to fight Islamic State militants.

Mr. Hagel declined at a Pentagon news briefing on Thursday to comment directly on the memo, but said he owed the National Security Council his best thinking on difficult issues like the U.S. strategy in Syria.

"This is a complicated issue," he said. "We are constantly assessing and reassessing and adapting to the realities of what is the best approach, how we can be most effective. That's a responsibility of any leader."

Moderate Syrian rebels complained earlier this week that they are losing control of towns and suburbs in and around the major cities of Damascus, Aleppo and Hama to Assad regime forces, which have launched a torrent of airstrikes of its own.

Mr. Hagel has complained before about administration decision-making. Earlier this year, he privately voiced concern that the U.S. was strengthening Russia's hand in Ukraine by publicly saying it would support Kiev's requests for aid, but then balking at providing lethal assistance and delaying other military support, like body armor and night vision equipment.

U.S. airstrikes have played an important role in the effort by Syrian Kurds to defend the border town of Kobani against an Islamic State offensive. Despite international attention on that fight, U.S. strategy in the region is primarily focused on Iraq.

There, the U.S. will eventually expand its effort to advise Iraqi forces into Anbar province, but only after the Iraqi government agrees to provide weapons to Sunni groups, said Gen. Martin Dempsey, the chairman of the Joint Chiefs of Staff, alongside Mr. Hagel.

"We need to expand the train-advise-and-assist mission into the al-Anbar Province, but the precondition for that is that the government of Iraq is willing to arm the tribes," Gen. Dempsey said.

Officials said expanding aid to Sunni groups was always part of the U.S. plan in Iraq. But Gen. Dempsey's comments were his most explicit yet about U.S. plans to step up support to Sunnis in Iraq's western province.

Gen. Dempsey said the U.S. is exploring how to bring an offensive capability to Sunni tribes willing to take up arms against Islamic State militants controlling much of Anbar province.

Defense officials said the effort could involve U.S. special operations forces, which now are working with Iraqi Shiites in Baghdad and Iraqi Kurds in Erbil. The effort also could involve advisers from other countries.

Gen. Dempsey believes there is more the U.S. can do in Anbar and with the Sunni tribes, according to a senior defense official. But the official said such an expanded effort is likely to fall short unless military gains by Iraqi security forces and political decisions by the Iraqi government keep pace.

Write to Julian E. Barnes at julian.barnes@wsj.com

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