Iraq is willing to mediate between Iran and Saudi Arabia, its foreign minister said, as a deepening diplomatic row between the two regional heavyweights continued.

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.

Zarif said Iran "wants no tension in the region and would always welcome dialogue with its neighbours".

Saudi Arabia broke off diplomatic relations with Iran after its embassy in Tehran was stormed by protesters angered by the kingdom's execution of a prominent Shia cleric, who was put to death along with 46 other mainly Sunni convicts on terrorism charges.

Though thousands of Iraqi Shias took to the streets on Tuesday to protest the execution of Nimr al-Nimr, Baghdad has taken a more cautious line.

Iran is a key ally of the Shia-led government in Baghdad, has helped it in the fight against the Islamic State of Iraq and the Levant group, and supports powerful Shia militias in the country.

At the same time, as the fight against ISIL enters its second year, Iraq is grappling with its worst political and security crises since the withdrawal of US troops in 2011.

Last week, Saudi Arabia sent an ambassador to Baghdad for the first time in 25 years.

Regional tensions should be faced "wisely, responsibly and rationally in order to preserve the security and stability of Iraq," Iraqi Prime Minister Haider al-Abadi said in a statement on Tuesday.

Source: Agencies