Barchi released a short statement Saturday:
"While Rutgers University stands fully behind the invitation to Dr. Rice to be our commencement speaker and receive an honorary degree, we respect her decision not to participate in the upcoming Rutgers University commencement, which she clearly articulated in her statement this morning.
"Now is the time to focus on our commencement, a day to celebrate the accomplishments and promising futures of our graduates," he said.
It was unclear who will replace Rice. More information "will be announced in the coming days," Barchi said.
Gov. Christie retweeted a link to the statement posted on Rice's Facebook page, adding: "As usual a class act by a great public servant."
In February, Rutgers' board of governors approved Rice's invitation, naming her the keynote speaker and recipient of an honorary Doctor of Laws degree. She was to receive a $35,000 honorarium.
Students and faculty had prepared a teach-in next week to discuss Rice's time as secretary of state; last Monday, dozens of students held a sit-in on the administrative building that houses Barchi's office.
In explaining her decision to withdraw, Rice said:
"I am honored to have served my country. I have defended America's belief in free speech and the exchange of ideas. These values are essential to the health of our democracy. But that is not what is at issue here."
Rice is a political science professor at Stanford University and teaches political economy in its Graduate School of Business. She is a former provost there.
Early in the controversy, Robert Boikess, a professor of organic chemistry who has been with Rutgers since 1968, wrote a resolution calling for the board of governors to "rescind its misguided decision." The Rutgers-New Brunswick faculty council passed the resolution in February.
"She basically said what we've said all along, which is that commencement should be a time of joyous celebration for the graduates and they don't need these kinds of political distractions," Boikess said Saturday, responding to the news of Rice's withdrawal. "We didn't object to her coming to Rutgers to speak. The problem was the honorary degree and the commencement speech."
Other professors spoke out against the resolution, as did some state officials, including State Sen. Joe Pennacchio (R., Morris) and Assemblywoman Mary Pat Angelini (R., Monmouth).
Student government held a debate, with the vote ultimately coming down in support of welcoming Rice.
Donald Coughlan, chairman of the New Jersey College Republicans, said his group was disappointed that Rice would not be speaking at the university.
Coughlan, a junior at Rutgers, said that universities "should be a place where free ideas are exchanged," and students need to listen to different voices.
He noted that the Rutgers University Student Assembly, the students' governing organization, had supported Rice's planned appearance.
In a statement Saturday, the Rutgers University College Republicans blamed "a small minority of the student body and intolerant professors" for protests against Rice.
"The students against her damaged university property and disrupted campus life this past week," it said, referring to glass that was broken at the university during a demonstration.
The statement said that in withdrawing from the controversy, Rice had shown "the humility and class that she demonstrated in her years of public service."
"We encourage the protesters to learn from her example," it said.
Members of the ad hoc coalition of students who held last week's sit-in questioned Barchi at a meeting Friday of the University Senate. Barchi agreed to meet with them, they said, and eight students from the group are scheduled to meet with him Monday morning.
"It's absolutely not over," said Amani Al-Khatahtbeh, a graduating senior from East Brunswick studying political science and Middle Eastern studies. "We're putting a lot into this meeting. We're really hoping that some positive changes can result."
Al-Khatahtbeh acknowledged that university administrators continued to stand by their invitation to Rice, but said Saturday's news was still a success because it indicated Rice had heard the students' opposition.
"Our voices made a difference," she said.
"That's what's so great about this: As a result of these protests, of the students voicing their concerns with the policies of her administration . . . I think that this is really setting a precedent for all public officials that they have people to answer to," she said.
Carmelo Cintron, another Rutgers-New Brunswick graduating senior who will be attending Monday's meeting, said part of his happiness with Rice's withdrawal was that students faced an uphill battle with the administration.
"There was always that . . . knowledge, that awareness within the group that this sort of decision is rarely overturned in this manner. We were conscious of the difficulty of the university in rescinding this invitation," said Cintron, who is studying comparative literature and philosophy.
Cintron said the student group would push for more transparency in the selection of future commencement speakers. At Monday's meeting, he said, they will ask Barchi to commit to allowing more input from the university community and following more open processes.
"To us, in the sense of her being commencement speaker . . . to us it's irrelevant . . . in the sense that we just didn't want her here," he said.
"Now, responding to the democratic processes that this has to be subject to?" he said. "That's still on the table. We're still fighting for that."
Inquirer staff writer Mark Fazlollah contributed to this article.