"If she's nominated to serve in such a serious position ... her nomination should be held until those questions are answered," Ayotte said.
Her comments are similar to those made by fellow Sens. John McCain (R-Ariz.) and Lindsey Graham (R-S.C.) on Wednesday.
McCain on Wednesday said Rice is "not qualified" for the position as top diplomat and promised he would attempt to block her possible nomination as secretary of State. Graham made similar comments.
Both senators have been highly critical of the role Rice played following the attacks against the U.S. Consulate in Benghazi, which resulted in the death of the U.S. ambassador to Libya.
“If Sen. McCain and Sen. Graham and others want to go after somebody? They should go after me. And I’m happy to have that discussion with them,” Obama said during his first post-election press conference on Wednesday.
Ayotte said that if Rice is nominated for the position — Obama has said he is still weighing the decision of who should replace outgoing Secretary of State Hillary Clinton — she should be judged on her answers to questions during the confirmation hearing.
But she rejected the argument that Rice has "nothing" to do with events in Benghazi, Libya, something Obama said in his defense on Wednesday.
According to Obama, Rice “was simply making a presentation based on intelligence that she had received" when she appeared on multiple networks following the embassy attacks.
During those interviews, Rice said the protest in Libya appeared to be spontaneous, despite the presence of heavy weapons, and prompted by an anti-Islam video on YouTube.
"He said she didn't have anything to do with Benghazi — then why would he send her out to every network?" Ayotte asked on MSNBC. "When you have a position like United Nations ambassador, why didn't she ask? ... She should have undertaken that responsibility."