Time is running out, Antonio Guterres told the 15-member Security Council
Iranian Foreign Minister Hossein Amir-Abdollahian arrived on Thursday in Riyadh, his first official Saudi trip since a landmark rapprochement in March, state media reported.
A Chinese-brokered deal saw the long-time rivals agreeing to restore diplomatic relations and reopen their respective embassies.
Iran and Saudi Arabia had severed ties in 2016 after Saudi diplomatic missions in the Islamic republic were attacked during protests over Riyadh's execution of cleric Nimr al-Nimr.
Amir-Abdollahian "arrived at Riyadh Airport a few minutes ago for a one-day trip, and was welcomed by the deputy foreign minister of Saudi Arabia," official news agency IRNA said.
The visit "is focusing on bilateral ties, regional and international issues", according to IRIB state broadcaster.
IRNA said Amir-Abdollahian was due to meet with his Saudi counterpart and other officials in the kingdom.
The minister was accompanied by the new Iranian ambassador to Saudi Arabia, the report added.
State media reported in May Tehran had named Alireza Enayati, a former ambassador to Kuwait, as the Islamic republic's Saudi envoy.
In June, Prince Faisal bin Farhan became the first Saudi foreign minister to travel to Iran since 2006.
Earlier that month Iran had reopened its embassy in Riyadh with a flag-raising ceremony.
On Wednesday, Iranian state media said military officials from both countries met in Moscow on the sidelines of a security conference.
Amir-Abdollahian has said this week that the new ambassador to Riyadh is accompanying him during Thursday's visit "officially start his mission".
On August 9, Iran said the Saudi embassy in Tehran had begun operations but Riyadh has yet confirm.
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