The Tehran Stock Exchange's benchmark TEDPIX index gained 49,870 points, rising more than 2.5%.
The index closed at 1,961,649 on Saturday after surging by over 57,325 points, or 3.01%, on the day, according to the Tehran Stock Exchange (TSE) website.
Nearly 13.6 billion shares changed hands in more than 2.5 million exchanges in the TSE, bringing over 235 trillion rials ($1 billion) to the market.
The Social Security Investment Company, Persian Gulf Petrochemicals, Mobarakeh Steel and Isfahan Oil Refinery had the highest positive impact on TEDPIX on Sunday.
The main index at Iran Fara Bourse, a subsidiary of the TSE for trading securities and other financial instruments, also rose by 535 points to reach 20,818 points.
In recent years, the Iranian stock market has been accompanied by various leaps, which have sometimes set world records.
One of the reasons why the TSE is still breaking records these days is the government's support for the capital market and encouraging people to invest in the stock market.
Directing manufacturing sector to apply new financial tools is one of the most important policies, which led to serious attention to the stock market.
Given the fact that the manufacturing sector needs capital and the banking sector fails to finance it all, big companies are after using new capacities in the capital market.
The massive influx of liquidity into the stock market has eliminated all the fundamental issues in this market's transactions and has caused the risks to reach their lowest level and leave no impact on preventing the stock market index from rising.
Reuters contributed to this story.