WASHINGTON—The Sunni militant advance in Iraq has reignited a debate in the Obama administration over its policy toward Syria, increasing pressure on the president to act more aggressively against a growing regional threat, according to current and former government officials.

Some argue that any U.S. military action against the Islamic State of Iraq and al-Sham, or ISIS, in Iraq will fall short if it doesn't hit the group's major strongholds in neighboring Syria. ISIS now occupies territory on both sides of the border.

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