Condoleezza Rice says "no way" to VP for Romney

UPDATED 8:20 a.m. ET

(CBS News) Condoleezza Rice is not interested in being Mitt Romney's running mate.

In an interview with "CBS This Morning," the former secretary of state said, "There is no way that I will do this," when asked if she would accept a position as the No. 2 on this year's Republican presidential ticket.

"Charlie, I didn't run for student council president. I don't see myself in any way in elected office. I love policy. I'm not particularly fond of politics," she told host Charlie Rose, adding that she thinks Romney has "terrific judgment."

Pressed on whether she would turn it down if asked, she said, "I'm saying there is no way that I will do this, because it's really not me. I know my strengths, and governor 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," she said.

Rice spoke over the weekend at a Utah retreat of big Republican donors for Romney and her remarks were widely praised by attendees.

"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," she said.

"I also talked about the essence of America, and I think perhaps that is what people resonated with, that this is a country in which people really believe that it doesn't matter where you came from, it matters where you're going and that we really need to concentrate on rebuilding our strengths as a country of immigrants, a country where it doesn't really matter your zip code so that you can get a good education, and the need to really pay attention to those strengths so that we can lead from an internal strength at home," she added.

Asked where she disagrees with President Obama on foreign policy, she said she understands "how hard it is to be in the White House," but said the United States cannot "lead from behind."

"The United States has to have a view, it has to gather people around that view, and frankly, I think we need to do more of that, and the last several years I think we've been lacking on that front," she said.

"And so, let's make alliance with those who understand that Syria will never be stable with Bashar al Assad in place. Let's help the opposition to organize. And Syria will be better off with(out) Bashar al Assad and so will the Middle East," she said.

"That's most of the states in the region and including some powerful states like Turkey that are now beginning to suffer from the instability," she said.