Riyadh's new Foreign Minister Adel al-Jubeir on Thursday criticised what he called Iran's "negative" role in the Yemen conflict, and repeated claims Tehran was providing arms and funding to anti-government forces.
Iran has long denied sending weapons to Shiite Huthi rebels in Yemen, with supreme leader Ayatollah Ali Khamenei saying this week that forces fighting supporters of exiled Yemeni President Abedrabbo Mansour Hadi did not need military support from Tehran.
Iran's foreign ministry spokeswoman Marzieh Afkham said allegations it was arming the Huthis "were nothing but efforts to put the blame on others based on repeated and unfounded analysis".
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A Saudi-led coalition has been conducting air strikes on Yemen rebel positions since late March and there are growing calls for an end to its aerial campaign as the death toll mounts in the impoverished nation.
Riyadh proposed a five-day humanitarian ceasefire on Thursday, but later warned the Huthis had crossed a "red line" by targeting southern Saudi Arabia with cross-border shelling.
Coalition air strikes on Thursday hit the Huthis' northern stronghold of Saada, Saudi state media reported.
Tensions between Shiite Iran and Sunni-ruled Saudi Arabia have been rising steadily, not only over Yemen but also the situation in Syria, Iraq, Lebanon and Shiite-majority but Sunni-ruled Bahrain.