Iran's foreign minister raised the water issue on Thursday during a telephone conversation with Amir Khan Muttaqi, the acting foreign minister of the Taliban.
Abdollahian has put pressure on the Taliban not to violate Iran's right to Helmand waters.
This senior Iranian diplomat had warned the group last month that Tehran would take legal measures if the Taliban does not provide Iran's water rights.
Abdollahian had said, "The full supply of Iran's water rights from the Helmand River plays a decisive role in our strategic policy towards the Taliban government in Afghanistan."
The semi-official Fars news agency stated that Iran and Afghanistan have been caught in a long-term water dispute, which has prevented understanding the vast potential of bilateral trade relations.
Kabul and Tehran signed a water sharing agreement on the Helmand River in 1973, according to which Afghanistan committed to deliver an average of 820 million cubic meters of water to Iran on an annual basis.
Iran has repeatedly criticized Afghanistan for not complying with the terms of the agreement.