ARSAL, Lebanon—As the Assad regime moves to take control of Syria’s last opposition strongholds, the government and its foreign backers are calling on millions of refugees who fled the bloody conflict to come home.

But obstacles the regime is throwing up to their return show that President Bashar al-Assad—mindful of the strain refugees are putting on neighboring countries—is willing to use the exiles as bargaining chips to secure foreign aid and sanctions relief, Western diplomats and analysts in Beirut say.

The...