The Iranian embassy noted that the AIIB officials had invited Iran's banking officials to attend the upcoming meetings of the bank.
Fifty-seven countries have applied for membership in the international bank and 34 have already been granted membership.
China is going to invest about $50 billion in the bank to hold about 50 percent of AIIB's shares.
Russia’s First Deputy Prime Minister Igor Shuvalov, speaking on Saturday at a forum in Boao on the Southern Chinese island of Hainan, said the country plans to join the AIIB.
Washington’s European allies including Britain, France, Germany and Italy have already also announced they would join the bank, leaving the US isolated, World Bulletin reported.
Other countries such as Turkey and South Korea have also said they would join. Brazil, China's top trading partner, said on Friday it would sign up.