Two Iranian military commanders visited a border area with Afghanistan following the heavy exchange of cross-border gunfire between Taliban and Iranian border guards, which killed and injured several.
Taliban spokesman and Iranian state media said two Iranian border guards and a Taliban fighter were killed during the skirmish over water rights.
The clashes occurred Saturday morning at the Sassuli border point in the Iranian province of Zabul.
The Iranian border guards said in a statement that its forces used their intense fire to inflict heavy casualties and severe damage without giving further details.
Taliban defense ministry spokesman Enayatullah Khowarazmi said: "Unfortunately, once again, in the border areas of Kong district of Nimroz province, there was a shooting by Iranian soldiers, (and) a conflict ... broke out."
"The Islamic Emirate of Afghanistan considers dialogue and negotiation reasonable for any problem. Making excuses for war and negative actions is not in the interest of any of the parties," Khowarazmi said.
Commander of the ground forces in the Iranian army Kioumars Heydari and deputy commander of Iran's Law Enforcement Forces Qasem Rezaei visited the border to monitor the situation.
Heydari said: "The common borders with Afghanistan are fully under the control of the army's ground forces... and security is fully established."
Iranian media confirmed the reopening of the Silk Road border bridge between Iran and Afghanistan, which was closed due to the clashes.
Rezaei asserted that Tehran would not allow any unfortunate incident on the border with Afghanistan, adding that stability has been restored.
He accused the Taliban of using all forms of weapons without observing international laws and the principle of good neighborliness.
Meanwhile, Assistant of Foreign Minister Rasool Mousavi said Iran must remain vigilant, warning any conflict will be a "strategic loss" for both parties.
Iranian media reported that officials from Iran and Afghanistan had agreed to a ceasefire and the formation of a fact-finding committee.
The Iranian parliament held an emergency meeting to discuss the tensions with the Taliban. Iran's special envoy to Afghanistan, Hasan Kazemi Qomi, attended the meeting.
Qomi had held talks with Taliban's Foreign Minister Amir Khan Muttaqi in Kabul Saturday.
Lawmaker and National Security and Foreign Policy Committee member Ismail Kothari said the dispute will be resolved through dialogue, not force. He clarified that Iran does not recognize the Taliban despite meeting with its members.
Meanwhile, the Taliban claimed to have destroyed 18 Iranian border installations, reported Russia Today.
It quoted a statement by the Taliban's Communications Department accusing the Iranian Revolutionary Guard Corps (IRGC) of carrying out the attacks.
The clashes reflect the sharply escalating rising tensions between the two countries amid a dispute over water rights over a dam on the Helmand River.
Last week, Iran warned that it reserves the right to take the necessary measures to protect its shares of the water.
It accused the Taliban of violating a 1973 agreement by reducing the water flow from the river to the dry eastern regions of Iran. The Taliban denied the accusation.
The Helmand River originates from central Afghanistan and flows over 1,000 km until it reaches Lake Hamun at the border.
Taliban spokesman Zabihullah Mujahid had previously said Kabul was holding on to fulfilling its obligations but indicated that the water level had declined because of a severe drought.