Sunni-Shiite tensions flared in the region in the wake of al-Nimr’s execution, with Shiites in Iran, Lebanon, and Iraq warning of repercussions. An outraged Shiite mob stormed the Saudi diplomatic mission in Tehran late Saturday.
"The security and stability of the whole Region, that is already facing great threats, is at stake," Mogherini said in phone talks with Iranian Foreign Minister Javad Zarif, as quoted by the European External Action Service (EEAS).
"No effort should be spared by all parties to keep the situation under control and to avoid sectarian tensions to escalate, they agreed," the EEAS statement said.
Sheikh al-Nimr was among 47 people convicted of terrorism whose execution was announced by the Saudi Interior Ministry on Saturday. He was sentenced to death on charges of inciting hatred and disobedience to the Saudi king in 2014.
Mogherini warned that continued tensions in the Middle East could further hinder cooperation between key regional powers on the Syrian peace process and in the fight against Islamist militants.
"These efforts should not be jeopardized by new instability," the EU foreign policy chief underscored.
Iran and Saudi Arabia have been at odds over political process in Syria and the role of Syrian President Bashar Assad in political transition, with Saudi authorities calling for his resignation.