Barzani, in his message, highlighted that Iran is an important neighbor for both the Kurdistan Region and Iraq.
The Kurdish PM expressed confidence that the two sides will continue to work together, building on existing ties and shared interests.
Pezeshkian won the 14th presidential election in Iran, securing a majority of the votes in the second round of voting.
He received over 16 million votes, defeating Saeed Jalili who received over 13 million votes.
Barzani's message follows a period of increased cooperation between Iran and the Kurdistan Region of Iraq, with both sides emphasizing the importance of good neighborly relations and shared economic interests.