The longtime senator would be almost certain to be easily confirmed by his colleagues on Capitol Hill.
If Obama taps Kerry for State, the president will create a potential problem for Democrats by opening a Senate seat — one that recently defeated Republican Sen. Scott Brown is eyeing. Brown had been elected as Massachusetts' other senator in January 2010 after Democrat Ted Kennedy died, stunning the political world as he took the seat held by Kennedy for decades. Brown lost that seat in the November election.
House Democratic women had cast the criticism of Rice as sexist and racist — she is African-American — and some expressed disappointment with the news.
"If judged fairly based solely on her qualifications for the job, she would've made an extraordinary secretary of state," said Rep. Karen Bass, D-Calif., a member of the House Foreign Affairs Committee.
Rice did not have a strong relationship with members of the Senate. Graham, who is the top Republican on the Appropriations subcommittee that handles foreign aid and the State Department, said he barely knew her.
In a brief statement, a spokesman for McCain said the senator "thanks Ambassador Rice for her service to the country and wishes her well. He will continue to seek all the facts surrounding the attack on our consulate in Benghazi."
Rice's decision comes ahead of the anticipated release next week of a report by an Accountability Review Board into the attack on the Benghazi mission. The report ordered by Clinton, focuses on the run-up to and the actual attack and is not expected to mention Rice's role in its aftermath.
Clinton is to testify about the report before Congress next Thursday.
At issue is the explanation Rice offered in a series of talk show appearances five days after the attack in Libya.