The talks in Tehran were focused on the issues related to both countries and also trade cooperation.
Szijjártó, also Hungary's trade minister, at the head of a trade delegation arrived in the Iranian capital late on Wednesday.
Szijjártó's Tehran visit took place at the invitation of his Iranian counterpart.
Later, the Hungarian minister of foreign affairs will hold a meeting with Iranian President Ebrahim Raisi.
The two countries' foreign ministers have already held talks on the sidelines of the UN General Assembly meeting in New York in September.
1483**2050
Follow us on Twitter @IrnaEnglish