By Justin Sink - 06/26/12 11:58 AM EDT
"I didn't run for student council president. I don't see myself in any way in elective office," Rice told "CBS This Morning" on Tuesday.
"I'm saying there is no way I will do this, because it's really not me, I know my strengths. Gov. Romney needs to find someone who wants to run with him, there are many people who will do it very very well and I'll support the ticket," Rice said.
When "CBS This Morning" host Charlie Rose pressed Rice, noting she hadn't technically said she wouldn't accept the offer to be vice president, the former secretary of State was more definitive.
"It's not going to happen — and no," she said.
Rice delivered a widely regarded policy briefing over the weekend to a meeting of the Republican presidential nominee's top donors, sparking talk that she was in the running for a spot on his ticket.
Rice, who has returned to her teaching job at Stanford University, was also pressed about her speech to Romney donors that drew widespread applause from attendees at the Utah retreat.
"I talked about the need for American leadership, I talked about the importance of the United States to a more peaceful world, a world that has been quite turbulent in recent years and needs a strong American anchor. But I also talked about the essence of America, and perhaps that's what people resonated with," Rice said.
She also championed the former Massachusetts governor's foreign policy credentials, arguing his core belief in a free market system would help the United States internationally.
"What Mitt Romney will bring to the presidency — and I believe he would be a very good president — is he would bring first and foremost an understanding of the role America has to play in the world," Rice said.
The former Bush official did give President Obama some credit for his tactics in continuing the war on terrorism.
"There's no doubt we have benefited really now from 10 years of relative consistency when it comes to the war on terror. President Bush left a lot of tools to President Obama. A military and intelligence integration that has worked exceedingly well as we were able to bring even [Osama] Bin Laden to justice," Rice said.
But the former secretary of State expressed concern over the handling of Syria, and Russian attempts to arm the Assad regime.
"You may not be able to get Russia to come to the table. Russians have a view under Vladimir Putin that is really a 19th century view of foreign policy: you intimidate your neighbors," Rice said.
She went on to echo Sen. John McCain's (R-Ariz.) call for American arming of rebel troops in the region, along with greater collaboration with allies like Turkey.
"I do believe that ultimately we're going to have to arm the opposition, maybe even today. Because people are being armed. Assad is being armed by the Russians and the Iranians," Rice said.