Staffan de Mistura was to arrive in Riyadh amid fears that the furor over the Saudi execution of a Shiite cleric could undermine international peace efforts in Syria.
De Mistura "believes that the crisis in Saudi-Iranian relations is a very worrisome development and stresses the need to ensure it does not cause a chain of adverse consequences in the region," said UN spokesman Stephane Dujarric.
Both Iran and Saudi Arabia are key players in the diplomatic push to end the nearly five-year war in Syria, with Tehran among President Bashar al-Assad's strongest allies while Riyadh is backing militias fighting Damascus.
Dujarric said the envoy would "assess the implication" of the crisis on the Syria peace effort.
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UN Secretary-General Ban Ki-moon said he was "deeply dismayed" by the Saudi execution of 47 people including prominent Shiite cleric Nimr al-Nimr, who has been critical of the Sunni royal family and was a driving force behind anti-government protests in 2011.
Saudi Arabia cut ties with Iran late yesterday, giving diplomats 48 hours to leave the country, after protesters set fire to its embassy in Tehran and a consulate in second city Mashhad.
"He stressed the importance of continued constructive engagement by both countries in the interest of the region and beyond."
In his talks with Saudi Foreign Minister Adel al-Jubeir, Ban urged Saudi Arabia "to renew its commitment to a ceasefire" in Yemen after the Riyadh-led coalition announced yesterday that it was ending the truce with Iran-backed rebels in the country.
The UN envoy for Yemen, Ismail Ould Cheikh Ahmed, was to hold talks in Riyadh on Wednesday to push for a renewed ceasefire.