Iran on Thursday accused Saudi warplanes of deliberately bombing its embassy in Yemen, in a new escalation of diplomatic tensions that have reverberated across the Middle East.

Shiite-dominated Iran also announced a ban on imports of all products from its Sunni-ruled rival, following a dramatic chill in relations that has triggered international alarm.

It comes days after Saudi Arabia broke off diplomatic ties with Iran in response to an arson attack on its own embassy in Tehran by protesters infuriated by Riyadh's execution of a prominent Shiite cleric.

Tehran said an unspecified number of embassy staff had been wounded in the raid on the rebel-held Yemeni capital Sanaa, which has been targeted by months of air strikes by a Saudi-led Arab coalition.

"This deliberate action by Saudi Arabia is a violation of all international conventions that protect diplomatic missions," Iranian foreign ministry spokesman Hossein Jaber Ansari said, quoted by state television.

"The Saudi government is responsible for the damage caused and for the situation of members of staff who were injured," Ansari added, without specifying when the alleged strike took place or the seriousness of the injuries.

"The Islamic republic reserves the right to pursue its interests in this matter," he said.

Iran also announced that a ban on Iranians travelling to the Saudi holy city of Mecca for the umrah pilgrimage would remain in place indefinitely.

Longstanding frictions between the Middle East's foremost Sunni and Shiite Muslim powers exploded into a full-blown diplomatic crisis at the weekend when Riyadh executed Shiite cleric and activist Nimr al-Nimr along with 46 others.

- Diplomatic fallout -

Nimr's death unleashed a wave of anger across the Shiite world, including in Iran where protesters stormed and set fire to the Saudi embassy in Tehran and consulate in the second city of Mashhad.

Iran denounced the attacks on the Saudi missions, but the repercussions quickly rippled across the region with Saudi allies Bahrain, Sudan and Djibouti also cutting diplomatic ties with Tehran.

The United Arab Emirates downgraded relations with Iran while Kuwait and Qatar recalled their ambassadors.

The Yemen conflict, which pits the pro-Iranian Huthi Shiite rebels 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.

They also support opposing sides in Syria, where Tehran has provided military assistance to its close ally President Bashar al-Assad against rebel groups, some backed by Saudi Arabia.

The growing tensions have heaped doubt on a UN-backed plan that foresees talks between the Syrian sides this month in a bid to end a war that has claimed more than a quarter of a million lives.

The roadmap, unanimously adopted by the UN Security Council, calls for the establishment of a transitional government within six months and elections within 18 months.

The Iran-Saudi crisis also threatens a fragile UN-backed initiative to end the war in Yemen, where the world body says at least 2,795 civilians have been killed since March.

UN envoy Ismail Ould Cheikh Ahmed has called for a new round of talks on January 14 but the sides have yet to confirm that they will attend.

At the same time the row has dealt another blow to the unity of the OPEC oil cartel, which includes both Iran and Saudi Arabia, at a time when a glut of crude on world markets has sent prices plunging.

The growing Middle East tensions have further reduced expectations of any action by OPEC to try to shore up oil prices.

With fears of weaker Chinese demand also mounting, New York's main crude contract slid to a 12-year low of $32.10 a barrel on Thursday.