The U.N. Security Council called on all sides to de-escalate the upsurge in violence and re-engage with U.N. political efforts to achieve a cease-fire without preconditions.
There was no independent confirmation, but pictures circulated on social media appeared to show Mr Saleh's body.
Yami called for a serious and resolute stance, and to move at all levels politically, diplomatically and militarily, to form a united Arab front.
The ICRC said on Tuesday that another 400 people have been wounded in the clashes, which first erupted last week as the alliance between the rebels and Saleh's followers crumbled. A spokesman quoted Aboul-Gheit as saying the worldwide community should label the Houthis a "terrorist" organization.
Iran's semi-official ISNA news agency quoted Gen. Mohammad Ali Jafari on Tuesday as saying that Saudi Arabia, "on behalf of the USA and the Zionist regime (Israel), has a very important role in creating insecurity" in the Middle East.
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Saleh, who ruled Yemen with an iron fist for three decades until 2012, had joined forces with the Shiite Huthi rebels three years ago when they took control of large parts of the Arabian Peninsula country including the capital Sanaa.
A military source said the Huthis stopped their four-car convoy about 40 kilometres south of Sanaa and shot dead Saleh and two other senior GPC officials.
Air raids also struck northern provinces including Taiz, Haja, Midi and Saada, the rebel-owned channel said, although there was no immediate word on casualties.
The end of the alliance between the Houthis and Saleh might have tilted the three-year civil war in favor of Yemen's internationally recognized government and the Saudi-led coalition.
The killing of Yemen's ex-President Ali Abdullah Saleh by the country's Shiite rebels as their alliance crumbled has thrown the almost three-year civil war into unpredictable new chaos.
The bloody conflict has left impoverished Yemen as the world's leading humanitarian disasters with millions of people facing starvation.
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Houthi officials said their fighters killed Saleh as he tried to flee the capital for his nearby hometown of Sanhan.
The Houthis and Saleh's forces began fighting each other in Sanaa last week.
The fighting has claimed more than 10,000 lives since then.
When Saleh left power, he stayed in the country and kept the loyalty of many military commanders, splitting the armed forces between himself and Hadi.
The Houthis seized Sanaa in September 2014, forcing the government of president Abdrabu Mansur Hadi to relocate to the southern city of Aden.
A least 234 people were killed in fighting that the International Committee of the Red Cross described as the fiercest since the start of the conflict. It is reported that only five people attended the funeral.
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