"In the present serious circumstances, I consider that the PAN should look for a leader, seeking a consensus. I am not fighting for just a right to lead, there are other men and women in high positions in the party, but I believe that in the PAN we will make the best decision," Zavala said in a statement published online Sunday.
The main goal for PAN, one of the top three political parties in Mexico, is to reconcile with civil society, she added.
Calderon, a PAN party member, was Mexican president from 2006-2012. His policies were built on a foundation of strong resistance to crime.
After stepping down from the presidency, Calderon accepted a yearlong fellowship offer from Harvard University in the United States.
At last week's parliamentary election, PAN received more than 20 percent of votes, some 10 percent behind the ruling Institutional Revolutionary Party.