The statement by the 15-member council, which called on Iran to protect diplomatic personnel and property, made no mention of the execution of Sheikh Nimr al-Nimr.
Saudi Arabia cut off diplomatic ties with Iran on Sunday after protesters ransacked and set fire to the Saudi Embassy in Tehran and the consulate in Mashhad.
"The members of the Security Council condemned in the strongest terms the attacks against the Kingdom of Saudi Arabias embassy in Tehran, and its Consulate General in Mashhad in the Islamic Republic of Iran, which resulted in intrusions into the diplomatic and consular premises, causing serious damage," said the council statement.
Expressing "deep concern" over the attacks, the council "called on the Iranian authorities to protect diplomatic and consular property and personnel, and to respect fully their international obligations in this regard."
Council members urged the sides to "maintain dialogue and take steps to reduce tensions in the region."
Saudi Ambassador Abdallah al-Mouallimi had earlier urged the council to "take all appropriate measures to ensure the inviolability of diplomatic facilities and the protection of all Saudi diplomats in Iran."
Iran, for its part, expressed "regret" after the attacks on Saudi posts.
In a letter to the UN Security Council, Irans mission at the United Nations vowed to "take necessary measures to prevent the occurrence of similar incidents in the future."
Riyadh also defended the execution of 47 men including Nimr, saying in a letter to UN Secretary General Ban Ki-moon that they were "granted fair and just trials without any consideration to their intellectual, racial or sectarian affiliation."
Concern is growing that the Saudi-Iranian rift could derail peace efforts in Syria and Yemen. Two UN envoys were dispatched to Riyadh to safeguard the gains made in the peace talks.
At Russias request, the council on Tuesday will discuss the conflict in Yemen after the Saudi-led coalition ended a ceasefire with Iran-backed rebels in the country.(*)
Editor: Heru Purwanto
Copyright © ANTARA 2016