"Iran has not just offered Afghan refugees and migrants incentives to fight in Syria, but several said they were threatened with deportation back to Afghanistan unless they did," said Peter Bouckaert, emergencies director at the New York-based HRW.
"Faced with this bleak choice, some of these Afghan men and boys fled Iran for Europe."
Shiite Iran is a staunch supporter of Assad and provides financial and military support to his regime.
The brigade, which is backed by the powerful Revolutionary Guards, is named after the daughter of the Prophet Mohammed whose mausoleum near Damascus is venerated by Shiites.
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But some reports say the Afghans have been offered residency and a monthly salary to fight for Iran.
The Islamic republic denies having any boots on the ground and insists its commanders and generals act as "military advisers" in Syria and Iraq.
However, funerals are regularly held across Iran for "volunteer" fighters from Iran, Afghanistan, and sometimes Pakistan.
Only 950,000 have refugee status in Iran and the rest have been deemed unqualified for asylum.
At least two dozen Afghans interviewed by the watchdog said they or their relatives had been recruited or coerced by the Iranian authorities to fight in Syria.
Six of them said Iranian forces had trained them or their relatives in military camps near Tehran and Shiraz in 2015.
Two of the six had joined voluntarily, while the other four said they or their relatives had been coerced or forced to fight.