An Afghan government official who did not want to be named said seven migrants had died and 30 were still missing, according to survivors who returned to Herat, a province in Afghanistan on the border with Iran.
The Afghan government said it has launched an investigation into claims that migrants attempting to enter Iran drowned after being forced into a river by Iranian border guards.
Dozens of Afghans had crossed into Iran illegally from western Herat province when the incident happened on Friday, local media said.
The Afghan Human Rights Commission on Sunday said it had spoken with survivors who accused Iranian forces of beating and torturing them.
"They were made to cross the Harirud river, as a result a number of them drowned and some survived," it said in a statement.
The government said Saturday that the foreign ministry was investigating the incident.
A government official who did not want to be named said seven migrants had died and 30 were still missing, according to survivors who returned to Herat.
The Iranian consulate in Herat dismissed the reports and said no Afghan nationals had been arrested in the area.
There are between 1.5 to 3 million Afghan refugees living and working in Iran, most of them as wage labourers on construction projects.
Tens of thousands returned to Afghanistan after the coronavirus outbreak, but as restrictions ease in badly-hit Iran, many are again seeking work there.