A search was launched on Sunday to retrieve the bodies of Afghan migrants from a river in a western province after reports that Iranian border guards tortured them and threw them into the river to stop them entering Iran.
Afghanistan's Foreign Ministry on Saturday said an inquiry had been launched.
A senior official in the presidential palace in Kabul said initial assessments suggested at least 70 Afghans trying to enter Iran from bordering Herat province were beaten and pushed into the Harirud river.
The Harirud River basin is shared by Afghanistan, Iran and Turkmenistan.
Doctors at Herat District Hospital said they had received the bodies of Afghan migrants.
"So far, five bodies have been transferred to the hospital," said Aref Jalali, head of Herat District Hospital.
"Of these bodies, it's clear that four died due to drowning."
The Iranian consulate in Herat denied the allegations of torture and drowning of dozens of Afghan migrant workers.
"Iranian border guards have not arrested any Afghan citizens," the consulate said on Saturday.
Iranian embassy officials in the Afghan capital Kabul were not immediately available for a comment.
Noor Mohammad said he was one of 57 Afghan citizens who were caught by Iranian border guards on Saturday when they were trying to cross into Iran in search of work.
"After we were tortured, the Iranian soldiers threw all of us in the Harirud river," Mr Mohammad told Reuters.
Shir Agha, who also survived the violence, said at least 23 of the 57 people thrown by Iranian soldiers into the river died.
"Iranian soldiers warned us that if we do not throw ourselves into the water, we would be shot," Mr Agha said.
Afghan officials said it was not the first time people had been tortured and killed by Iranian police guarding the 920-kilometre border.
"Our people are not just some names you threw into the river," Herat's Governor, Sayed Qatali, said in a tweet to Iranian officials. "One day we will settle accounts."
The incident could trigger a diplomatic crisis at a time when the coronavirus pandemic has led to a mass exodus of Afghan migrants from Iran, with many testing positive for Covid-19.
Up to 2,000 Afghans a day cross the border from Iran, a global coronavirus hotspot, into Herat.
As of Sunday, at least 541 infected people are from Herat province, which recorded 13 deaths.
Most of the positive cases were among Afghans returning from Iran, said Rafiq Shirzad, a health ministry spokesman in Herat.