"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.
Jubeir said relations with Tehran had deteriorated "due to the sectarian policies" followed by Shiite-dominated Iran and "its support for terrorism and implanting of terrorist cells in the countries of the region".
"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.
In a joint statement, ministers meeting in Riyadh urged Iran to respect the landmark nuclear deal it reached with world powers, including curbs on ballistic missiles, as Tehran defiantly fired two more missiles on Wednesday.
The ministers "stressed the importance of implementing the (UN) Security Council Resolution 2231 concerning the nuclear deal, including what concerns ballistic missiles and other weapons," it said.
US Vice President Joe Biden said Wednesday that the United States would take action against Iran if the missile tests were confirmed.
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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.
They also support rebels in Syria's five-year-old war while Tehran openly backs the regime of President Bashar al-Assad.
Gulf nations had recently classified Iran-backed Lebanon's Shiite Hezbollah movement, classifying the militia as a terrorist group.
Saudi Arabia recently blocked $3 billion in military aid to Lebanon and urged its citizens to leave the country.
Jubeir said Lebanon is now run by Hezbollah.
"What is disturbing in the Lebanon question is that a militia that is classified as terrorist controls decision-making in Lebanon," he said.
Jubeir criticised a recent decision by a Lebanese court to release a Syria-linked former minister who is facing charges of having planned "terrorist" acts.
Michel Samaha's release "does not positively indicate that the army is independent of Hezbollah's influence," he said.
Asked about further Gulf sanctions against Hezbollah, Jubeir said the foreign ministers of the Gulf Cooperation Council had decided to look into measures that "would prevent Hezbollah from benefitting from GCC states".
Riyadh and its Gulf Arab allies have stepped up sanctions against Hezbollah and its alleged leaders since 2013 in retaliation for its intervention in the Syrian war to support Assad.
Last month Saudi Arabia froze the assets and prohibited dealings with three Lebanese nationals and four companies, in its latest action against Hezbollah.