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“We had a pretty terse meeting with Maliki here,” said Mr. Corker, referring to the prime minister’s visit to Washington in October.

Speaking at a hearing on Capitol Hill, Mr. Corker said Mr. al-Maliki “has not done a good job of reaching out to the Sunni population, which has caused them to be more receptive to al Qaeda efforts.”

That reception for ISIL has appeared only warm since Mr. al-Maliki won a third term as Iraq’s prime minster in May.

A senior Democrat on Capitol Hill also raised concerns Wednesday about the Iraqi leadership, as well as the nation’s proximity to both Iran and to the violent civil war that has gripped Syria during recent years.

“Clearly, we must continue to support Iraqi security forces, but I’m concerned by reports that they have been using barrel bombs in their operations,” said Sen. Robert Menendez, New Jersey Democrat and committee chairman.

Mr. Menendez said there are serious questions about a host of factors, including Iraq’s role in Syria, the activities of Iraqi Shia militias fighting with Syrian President Bashar Assad’s security forces and Iranian influence in Iraq.

Iranian airlines canceled all flights between Tehran and Baghdad due to security concerns, and Iranian leaders intensified security measures along the Shiite nation’s borders, according to the Iranian government-run IRNA news agency.

Ben Wolfgang contributed to this article, which is based in part on wire service reports.