The call was made by Ali Reza Enayati on his X account on Tuesday.
Enayati wrote in the day after his meeting with the Saudi deputy foreign minister Waleed Al-Khuraiji.
He said he held talks with the Saudi official on regional and bilateral issues.
In the meeting, the Iranian ambassador congratulated Al-Khuraiji on the Saudi National Day on September 23.
The first Iranian group of Umrah (minor) Hajj pilgrims embarked on the spiritual journey to Mecca, Saudi Arabia, on April 22 after about a 10-year hiatus.
In March 2023, Iran and Saudi Arabia jointly announced the resumption of diplomatic relations after seven years of tensions.
MNA/IRN