The handwritten letter covered “joint co-operation between the two friendly nations in various fields within the good bilateral relations that unite them”, Oman's News Agency (ONA) reported.
Mr Amirabdollahian met Oman's Sultan Haitham and is set to hold meetings with other Omani officials.
“Oman is a centre of regional dialogue on a diversified range of issues and high-ranking Omani authorities have always played a considerate role in relation to regional crises”, Mr Amirabdollahian said.
Yemen will be among the issues to be discussed by Iran's Foreign Minister and Omani officials, Iranian state media said.
The UN accuses Iran of smuggling weapons to Houthi militants through Oman.
In November, the US 5th Fleet said it intercepted a “large quantity” of explosives, including more than 70 tonnes of ammonium perchlorate, which is used to make rocket fuel, travelling in the Gulf of Oman to Yemen from Iran.
Iran is facing a third month of nationwide protests after the death of 22 year-old Kurdish-Iranian Mahsa Amini in police custody. She was arrested by the country's morality police for allegedly not abiding by the country's dress code.