NASHVILLE  Sarah Palin said in an interview broadcast Sunday that she would consider a run for the White House in 2012 “if I believe that that is the right thing to do for our country and for the Palin family.”

“It would be absurd to not consider what it is that I can potentially do to help our country,” Ms. Palin told Chris Wallace on “Fox News Sunday” in an interview recorded a few hours before she gave the keynote address at the National Tea Party Convention in Nashville. “I won’t close the door that perhaps could be open for me in the future.”

Those words were buttressed by the response she received at the convention on Saturday night. As Ms. Palin left the stage, the crowd erupted into chants of “Run, Sarah, Run.”