"The invitation was made during a trip by the deputy foreign minister in charge of Asian and Oceanic affairs (Mohammad Ali Fatollahi)," foreign ministry spokesman Ramin Mehmanparast told reporters at a weekly press briefing in response to a question.
"We are hopeful the visit will take place to serve as a leap forward in cooperation between the two countries, particularly in the economic field," he added. He gave no more details.
The United States fears that both Iran and North Korea will become nuclear-armed countries.
North Korea has demanded international recognition as nuclear-armed state but proliferation experts say that while it has enough plutonium for weapons it does not have the ability to place a weapon on a missile.
Iran, which unlike North Korea is a member of the Nuclear Non-Proliferation Treaty, could face more United Nations sanctions for enriching uranium.
Tehran, one of the world's biggest oil and gas producers, says this is for generating electricity but Washington and its allies fear Iran wants to acquire weapons capability.
Kim was in China this week on his first trip abroad since a suspected stroke in 2008.
