Iran's Kabul embassy and Herat consulate were targeted in demonstrations following unconfirmed footage posted online that appears to show attacks on Afghan refugees in Iran.
Demonstrators shouted, "Death to Iran" at the Kabul embassy, while protesters in the western city of Herat threw stones, destroyed cameras and set the Iranian flag alight. The Herat rally was broken up by the Taliban.
Eleven Iranian diplomats and a state news agency journalist were murdered in Taliban-controlled Mazar-i-Sharif in 1998, leading to a breakdown in relations between the Afghan fundamentalist group and Tehran.
Acting Taliban Foreign Minister Amir Khan Muttaqi passed on his dismay about the protests on Monday, according to Iranian news agency Tasnim.
It came during a phone call between Muttaqi and his Iranian counterpart, Hossein Amirabdollahian, where the Taliban official assured that Iran's diplomatic buildings and personnel would be protected from protesters.
In an apparent reference to footage of Afghan refugees being attacked in Iran, Amirabdollahian decried "propaganda" aimed at rupturing ties between Kabul and Tehran.
Iran's foreign ministry has asked the Taliban - which took over Kabul last summer - to prevent Afghans from entering Iran illegally and to adhere to deals reached between the two countries on water and other issues.
Amirabdollahian praised the Taliban for outlawing drug production and said he would like to see collaboration between the two countries on stopping drugs from being trafficked.
The previous Taliban administration played a key role in the production of heroin but has vowed to clampdown on the trade.