Saudi Foreign Minister Prince Saud al-Faisal told Kerry that Assad, a secular leader who belongs to the Alawite sect, an offshoot of Shiite Islam, has waged "genocide" through the more than two-year conflict that has claimed nearly 100,000 lives.
"The kingdom demands a clear, unequivocal international resolution that bans any sort of weapons support for the Syrian regime and declares null and void the legitimacy of that regime," Faisal said at a joint news conference.
"The regime's illegitimacy eliminates any possibility of it being part of any arrangement or playing any role whatsoever in shaping the present and future," he said.
Faisal voiced dismay at the role of rival Iran, which has poured assistance to Assad to save its main Arab ally. Hezbollah, the Lebanese Shiite Muslim group backed by Iran, is fighting in support of Syrian government forces.
"Syria is facing two things -- unprecedented genocide in this region and a foreign invasion," Faisal said. "What led to this situation are simple and basic demands by the Syrians to make their lives a little better."
Kerry has previously voiced fears of "ethnic cleansing" in Syria. But concern also lies among many Alawites and other minorities who believe Assad's fall would unleash a torrent of revenge attacks by militants of the Sunni majority.
President Barack Obama has vowed to step up support for the rebels after concluding that Assad defied warnings and used chemical weapons. But he is cautious about deeper involvement in an increasingly sectarian conflict.
US policymakers have privately expressed concern that Saudi Arabia and fellow monarchy Qatar could embrace hardline Sunni guerrillas, especially if they sense that Western support to mainstream rebels is ineffective.
Asked about Saudi Arabia's role, Faisal said the kingdom would help the rebels "in the most effective way that we can."
"The only restriction there is on the aid we can give to the Syrian opposition is our ability to help," he said.
Despite Faisal's tough line, Kerry said the United States supports an agreement last year in Geneva that would create a transitional government that includes both the rebels and regime, although not Assad himself.
"We believe that the best solution is a political solution in which the people of Syria have an opportunity to be able to make a choice about their future," Kerry said.
"We believe that every minority can be respected, there can be diversity and pluralism and that the people can do so in a climate of peace," he said.
Saudi Arabia, while a longstanding US ally and oil provider, practises a puritanical form of Wahhabi Islam and has some of the world's most sweeping restrictions on freedom of religion.
US officials have in the past voiced concern about money from Gulf Arabs funding Sunni hardliners in Afghanistan, Pakistan and elsewhere.
Kerry also paid his day trip to Jeddah to compare notes on the Middle East peace process -- one of his key priorities -- and on the chaotic politics of Egypt, where Saudi Arabia is considered to hold influence.
Kerry voiced hope that weekend demonstrations planned against President Mohamed Morsi would be peaceful and encouraged action by the government on measures including structural reforms to revive a moribund economy.
"We will obviously hope that it will not produce violence and be a moment of catalysing positive change in Egypt," Kerry said.
Kerry arrived later Tuesday in Kuwait and heads Wednesday to Jordan. He added a stop for Saturday in the United Arab Emirates, his spokeswoman Jen Psaki said.
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