McCain said the "information that she gave the American people was incorrect."
In a statement after the meeting, which also included Acting CIA Director Michael Morrell, Rice said the two stressed that "neither I nor anyone else in the administration intended to mislead the American people at any stage in this process, and the administration updated Congress and the American people as our assessments evolved."
After Rice had withdrawn, an administration official voiced frustration that Rice had been unfairly targeted over Benghazi.
"It's absolutely a fact that she had nothing to do with the security presence in Benghazi and the intelligence collection or assessment. All she did was some interviews using cleared talking points that reflected our best understanding of the situation as we knew it at that time," the official said. "The fact that four people died in Libya is a tragedy, but Susan Rice had nothing to do with that tragedy. The fact that they focused on her talking points is a disservice to everyone who cares about this issue."
After Rice's announcement, Graham released a statement saying, "I respect Ambassador Rice's decision. President Obama has many talented people to choose from to serve as our next secretary of state."
Graham added that he would continue to try to get the bottom of the Benghazi matter.
Obama had fiercely defended Rice since Republicans first began to question her nomination -- first in the second presidential debate and later in his first news conference after his re-election.
He continued his support in a statement responding to Rice's decision.
"I have every confidence that Susan has limitless capability to serve our country now and in the years to come, and know that I will continue to rely on her as an adviser and friend," the president said. "While I deeply regret the unfair and misleading attacks on Susan Rice in recent weeks, her decision demonstrates the strength of her character, and an admirable commitment to rise above the politics of the moment to put our national interests first."