The US state department has urged Carter not to violate foreign policy by meeting Hamas's political leader.
Rice, who has sought Carter's advice on Middle East negotiations in the past, described Hamas as "terrorist organisation", that has refused "opportunities to come into line with international standards concerning the Middle East".
The US has demanded that Hamas, which controls the Gaza Strip, renounce violence, recognise Israel, and accept previous agreements between Israel and the Palestinians.
Barack Obama, the US Democratic presidential hopeful, said he will not criticise Carter, although he said he would not meet the Palestinian group.
"I'm not going to comment on former president Carter. He's a private citizen. It's not my place to discuss who he shouldn't meet with," Obama said.
Carter has not publicly backed either candidate in the Democratic race but hinted recently that he supports Obama.