"If Iran changes its way and its policies, nothing would prevent turning a page and building the best relationship based on good neighbourliness, with no meddling in the affairs of others," he told reporters in Riyadh.
"There is no need for mediation" in such a case, said Jubeir, whose country severed all links with the Islamic republic in January after crowds attacked the kingdom's diplomatic missions in Iran.
"Iran is a neighbouring Muslim country that has a great civilisation and a friendly people, but the policies followed that the revolution of (Ayatollah Ruhollah) Khomeini have been aggressive," he said.
Jubeir was speaking after a meeting for Gulf foreign ministers and their counterparts from Jordan and Morocco.
Sunni powerhouse Saudi Arabia and fellow Gulf nations also accuse Iran of supporting Shiite rebels in Yemen, as well as attempting to destabilise their own regimes.