"The Secretary-General reiterated that the attack on the Saudi embassy in Tehran was deplorable, but added that the announcement of a break in Saudi diplomatic relations with Tehran was deeply worrying," UN Spokesman Stephane Dujarric told reporters on Monday, Reuters reported.
Dujarric said that Ban said this to Saudi Foreign Minister Adel al-Jubeir in a telephone call.
"The Secretary-General urged both foreign ministers to avoid any actions that could further exacerbate the situation between the two countries and in the region as a whole," Dujarric added, saying that Ban also spoke with Iranian Foreign Minister Mohammad Javad Zarif on Sunday.
"He stressed the importance of continued constructive engagement by both countries in the interest of the region and beyond," he said.
The point of Ban's calls, Dujarric said, was to help ensure that both Iran and Saudi Arabia continue their commitment to ending the conflicts in Syria and Yemen.
"(The United Nations) will be pushing forward and very much hoping that the current tensions will not impact negatively on the two peace processes," Dujarric said.
The Saudi government on Sunday announced that Riyadh is severing its diplomatic relations with Tehran following angry protests in Tehran at the execution of Sheikh Nimr by Riyadh.
Speaking on Iranian state television, Iranian Deputy Foreign Minister for Arab and African Affairs Hossein Amir Abdollahian said in Tehran's first response that by cutting diplomatic ties, Riyadh could not cover up "its major mistake of executing Sheikh Nimr".
Saudi Arabia’s execution of 47 prisoners, including Sheikh Nimr, on Saturday drew global condemnation.
The executions took place in 12 cities in Saudi Arabia, four prisons using firing squads and the others beheading. The bodies were then hanged from gibbets in the most severe form of punishment available in the kingdom's law.
Sheikh Nimr had been detained in July 2012 on charges of delivering anti-regime speeches and defending political prisoners.