Iran's President Hassan Rouhani said the two countries could "cooperate on resolving regional and international issues, especially on fighting terrorism", the official IRNA news agency reported.
"The flow of arms and financial resources to terrorism must be stopped," Rouhani said.
Steinmeier's visit comes after a landmark deal between Tehran and world powers to limit Iran's nuclear programme in return for lifting international sanctions against it came into force last month.
The Gulf kingdom severed all ties with Iran last month after demonstrators stormed its embassy in Tehran and consulate in second city Mashhad following Riyadh's execution of a prominent Saudi Shiite cleric.
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