Talks between Middle East regional rivals Tehran and Riyadh have led to "serious progress" on the issue of Gulf security, an Iranian foreign ministry official said.

"Serious progress has been made on the subject of security in the Gulf," state news agency IRNA on Thursday quoted ministry spokesman Saeed Khatibzadeh as saying.

Shiite-majority Iran and Sunni kingpin Saudi Arabia, on opposing sides in multiple regional conflicts, have been engaged in talks since April with the aim of improving relations, for the first time since cutting ties in 2016.

The discussions were launched under Iran's former moderate president Hassan Rouhani and have continued since his ultraconservative successor, Ebrahim Raisi, took office in August.

Speaking to journalists on the sidelines of the UN General Assembly in New York, Khatibzadeh said the talks were "good" and called for countries to settle regional issues between themselves, without foreign interference. 

In Yemen, Iran supports Shiite rebels who still control most of the north, including the capital Sanaa, despite more than six years of Saudi-led military efforts to oust them.

Tehran has also been the main regional backer of Syrian President Bashar al-Assad against Sunni rebels since civil war broke out in 2011.

In Lebanon, Iran-backed Shiite group Hezbollah plays a pivotal role in political life, while its fighters have been heavily involved in neighbouring Syria in support of Assad's government.

Saudi King Salman on Wednesday expressed hope that talks with Iran would "lead to tangible outcomes to build trust" and to the relaunch bilateral "cooperation".

In a speech via videoconference to the General Assembly, the Saudi ruler again called on Tehran to cease "all types of support" for armed groups in the region, and reaffirmed his kingdom's support for "international efforts aimed at preventing Iran from developing nuclear weapons".

Riyadh -- an ally of Tehran's arch-foe Washington -- has concerns about Iran's nuclear programme, despite the Islamic republic's insistence it is pursuing only "peaceful" nuclear technology.