"Iran will bring terrorists and their masters to justice", he wrote on Twitter.
Chahbahar is located in the Sistan and Balochistan province of Iran close to the Pakistani border.
India on Thursday strongly condemned the "despicable" terrorist attack in the southeastern Iranian port city of Chabahar and said the perpetrators of the crime must be brought to justice expeditiously.
The broadcaster said a suicide bomber drove his explosives-laden vehicle into a police headquarters in the city.
The gunmen who attempted to storm the building were killed by security forces, Iranian media reported.
Many nearby shop owners and civilian passers-by, including women and children, were severely wounded, he added.
India is developing the Chabahar Port, to increase Chabahar's port capacity from 2.5 million tons to 8.5 million tons per year, to foster trade with Afghanistan and Central Asian countries by-passing Pakistan.
Mohammad Pakpur, the commander of the ground forces of Iran's Islamic Revolutionary Guards Corps (IRGC) said the attack had failed.
The news agency carried pictures of the remains of the vehicle used by the attackers which is believed to have been a blue Nissan van.
That operation followed a 2009 terror attack by extremist terrorists that claimed over 40 lives in Sistan-and-Baluchestan Province.
Iranian Interior Minister Abdolreza Rahmani Fazli also issued a statement in condemnation of the Chabahar terror assault, saying the "savage attack" proved again that the "evil hegemonic system would spare no plot" to target the nation.
In October, the group claimed the capture of 12 Iranian security personnel who were conducting an operation near the Pakistan border.
Last year, in the first deadly assault claimed by Islamic State in Tehran, 18 people were killed at the parliament and mausoleum of Ayatollah Ruhollah Khomeini, founder of the Islamic Republic.