As the administration prepares for another summit meeting between President Donald Trump and Russian President Vladimir Putin, there is division within the U.S. ranks over Moscow’s intentions and whether the two sides will be able to cooperate on a range of issues including the conflict in Syria.

Mr. Trump has expressed hopes of working more closely with Russia in Syria, where Moscow has played a central role in cementing President Bashar al-Assad’s power. The administration raised the issue with Mr. Putin’s government during...