"We urge both countries to engage in dialogue," German government Spokesman Steffen Seibert told a regular news conference, Reuters reported.
"We call on both countries, Saudi Arabia and Iran, to use all possibilities to improve their bilateral relations,” he added.
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.