By Elise Viebeck - 07/13/12 05:12 PM EDT
Dannenfelser added that the Romney already pledged "in no uncertain terms" to choose a running mate who opposes abortion rights.
Speculation that Rice is a leading contender for the VP spot grew after a report from a powerful conservative news aggregator.
Campaign buzz from The Drudge Report tends to carry extra weight because of personal connections between the site and Romney aides. It stated that Romney's choice would be announced in the "coming weeks."
Former Alaska Gov. Sarah Palin (R) notably praised the former secretary of State and said she would make a "wonderful" vice president in spite of her stance on abortion.
"I would certainly prefer a presidential and vice presidential candidate who had that respect for all innocent precious purposeful human life,” Palin said on Fox News. "We need to remember, though, that it’s not the vice president that would legislate abortion and that would be Congress’s role, and we’ll keep that in mind.”
But the SBA List, on Friday, disagreed.
With its statement, the group linked to a video of Romney saying in 2011 that his VP pick would agree with him on abortion and gay marriage.
"The person that I would select in that position would share my views on those important issues," Romney said, speaking at the Palmetto Freedom Forum.
In a rare move for leading Republicans, Rice has called herself "mildly pro-choice" — saying she is against late-term abortions and for parental notification.
In 2005, an interviewer said her stance would bar her from GOP politics. She replied: "I'm not trying to be elected."
Rice has also flatly denied that she would agree to join Romney's ticket.
The SBA List endorsed the former Massachusetts governor in April and promised to spend $10 to $12 million "mobilizing pro-life voters to ensure victory" in battleground states.
"We have taken Governor Romney at his word and therefore believe Secretary Rice will be ruled out of consideration," Dannenfelser said in her statement Friday. "Secretary Rice's position violates criteria that Governor Romney himself has laid out."