Several Saudi allies have followed the kingdom's lead and scaled back or cut diplomatic ties to Iran.
Ibrahim al-Jaafari was speaking on Wednesday in a joint press conference with Iranian Foreign Minister Mohammad Javad Zarif, who appeared to indicate that Tehran was open to resolving the stand-off.
Chinese Deputy Foreign Minister Zhang Ming is now in Saudi Arabia and will travel on to Iran, a ministry spokesman told reporters. Earlier protesters stormed the embassy and set parts of it alight.
Iran's top leader, Ayatollah Ali Khamenei, predicted "divine vengeance" for the execution of al-Nimr, an outspoken opponent of the ruling Al Saud family.
Anger in both countries is running high after the execution of a prominent Shiite cleric by Saudi Arabia last Saturday.
Iran on Thursday said Saudi Arabia warplanes had attacked its embassy in Yemen's capital.
The visit came after the crisis between Saudi Arabia and Iran widened on Tuesday when Kuwait recalled its ambassador to Tehran and Bahrain severed air links with the Islamic republic.
The Yemeni conflict, which pits the rebels known as Huthis against pro-government forces backed by Riyadh and other Gulf Arab states, is one of the main sources of dispute between Saudi Arabia and Iran.
"Obviously, it's something that we're concerned about, and that's why the secretary has spent so much time on it", he said, referring to Secretary of State John Kerry.
Tehran announced Thursday it was banning imports of goods from Saudi Arabia in response to the incident.
Iranian state television made the announcement Thursday.
The statement condemned the stories run by the Iranian media and the accusations against Erdogan, and demanded an end to such publications and broadcast that aim to create a negative image of the Turkish president in the minds of Iranians. That could spark further unrest, as witnesses in eastern Saudi towns have reported hearing gunfire overnight and armoured personnel carriers have been seen driving through neighbourhood streets.
The executions, which drew global condemnation, took place in 12 cities in Saudi Arabia, four prisons using firing squads and the others beheading.
Four share lead in La Quinta
CareerBuilder is in its first year as the title sponsor of the event long called the Bob Hope Classic, taking over for Humana. McIlroy laid down a marker of his own in his first event of the year after a two-month break and laser eye surgery.
'World looking forward to Tehran returning to its senses'
