Allies of Mrs. Clinton, who plans to make gender a central part of her appeal, call this a cynical ploy. Ms. Fiorina, they say, is being put to use by a Republican Party that is desperate to damage Mrs. Clinton without antagonizing female voters.

“These guys really believe it’s unfair that women are now running,” said Ann Lewis, a senior adviser to Mrs. Clinton in her 2008 campaign.

Speaking after Ms. Fiorina had just ridiculed Mrs. Clinton’s travel pace as secretary of state at the Iowa event, Ms. Lewis said: “Carly Fiorina went only to show she could be mean to Hillary.”

And Adrienne Elrod, a spokeswoman for Correct the Record, a group set up to defend Mrs. Clinton, dismissed Ms. Fiorina as “short on substance, with sophomoric one-liners,” in contrast to Mrs. Clinton’s “forward-thinking agenda and lifetime of work fighting for children and families.”

In an interview, Ms. Fiorina, 60, said she was not seeking the approval of Republican leaders. “The party is not leaning on me to do anything, and I didn’t ask the party’s permission,” she said.

But she did not shy away from arguing that her gender, along with her having worked her way up from a secretary to chief executive of Hewlett-Packard, made her particularly well positioned to go after Mrs. Clinton.