Custodian of the Two Holy Mosques King Salman bin Abdulaziz Al Saud and Crown Prince Mohammed bin Salman bin Abdulaziz
According to the Saudi News Agency (SPA) Thursday, the letters were received by Deputy Minister of Foreign Affairs Walid bin Abdul-Karim Al-Khuraiji during his reception of the Iranian Ambassador to the kingdom Ali Reza Enayati.
Issues of common interests and relations between the two countries were discussed during the meeting, SPA reported
Earlier this month, Saudi Arabia's ambassador to Iran arrived in the Islamic republic, and his counterpart landed in Riyadh, cementing ties between the Gulf rivals after a seven-year rupture in relations.
Saudi Arabia recognises the "importance of strengthening ties, increasing engagement... and taking the (relationship) to broader horizons," Ambassador Abdullah Alanazi said upon his arrival in Tehran to take up his duties, according to a Saudi foreign ministry statement on that day.
Alanazi was Saudi Arabia's ambassador to Oman, while Enyati was Iran's Kuwait envoy.
Saudi Arabia's Embassy in Tehran resumed operations last month. In June, Iran marked the reopening of its embassy in Riyadh with a flag-raising ceremony.
Shia-dominated Iran and Sunni Muslim Saudi Arabia agreed to resume diplomatic relations and reopen their respective embassies following a China-brokered deal in March.
Riyadh and Tehran severed ties in 2016 after Saudi diplomatic missions in Iran were attacked during protests over Riyadh's execution of Shia cleric Nimr Al-Nimr.
Last month, Iran's top diplomat, Foreign Minister Hossein Amir-Abdollahian, preached unity and dialogue during his first visit to Saudi Arabia since the surprise rapprochement was announced, saying bilateral ties were "progressing in the right direction."