(CNN) Sen. Elizabeth Warren has a message for those attacking her as angry: Yes, she is.

On Friday afternoon, the Massachusetts Democrat, in a fundraising email for her presidential campaign, addressed the innuendo stoked this week by former Vice President Joe Biden and others who have cast her as a elitist ideologue.

"I am angry and I own it," the subject line read.

"Over and over," Warren wrote below, "we are told that women are not allowed to be angry. It makes us unattractive to powerful men who want us to be quiet."

It was the most direct response to -- and an embrace of -- an attack launched by Biden in a Medium post on Tuesday in which he assailed the senator, without naming names, over her suggestion that his arguments against "Medicare for All" sounded like they were coming from a candidate "running in the wrong presidential primary."

In her response, Warren also made explicit what many of her supporters have suggested in recent days: that recent criticisms lodged against her by rivals like Biden and South Bend, Indiana, Mayor Pete Buttigieg have a sexist edge to them.

Both have singled out Warren for taking a "my way or the highway" approach to her campaign. On Tuesday, Biden wrote that Warren's remarks accusing him of employing "Republican talking points" against Medicare for All suggested a more damning analysis.

"These kinds of attacks are a serious problem. They reflect an angry unyielding viewpoint that has crept into our politics," the former vice president wrote, before describing Warren's "approach to politics" as "condescending" and elitist.

The word that jumped off the screen to many Democrats -- and a lot of women: "angry." Almost immediately, a series of writers and pundits zeroed in on and denounced the phrasing as sexist -- which, to many observers of her campaign, seemed odd, if not plainly misleading.

"This is not an endorsement of Elizabeth Warren the candidate, but an affirmation of who I know her to be. Anyone falsely casting her as angry & antagonistic is telegraphing the limits of their minds, & the magnitude of their insecurities," wrote journalist Connie Schultz , who is the wife of Sen. Sherrod Brown of Ohio.

'That has nothing to do with it'

In an interview with CNN's Dana Bash on Friday, after Warren's email landed, Biden denied that he had characterized his rival for the nomination as angry because of her gender.

"The strong women in my life are angry -- they get angry about things. That has nothing to do with it," he said.

Criticizing her in terms used to denigrate women, Biden added, was "not anything that I did or was intended to do."

"It had nothing to do with that," the former vice president said. "It had to do with the fact that it started off and she said, you know, Biden is running in the wrong primary because I disagreed, disagree with her Medicare for All proposal."

The Biden campaign's view -- and those of his close allies, men and women -- is that Warren threw the first punch, during the health care dust-up, and he is merely answering her remarks.

Warren's initial comment about running in the "wrong presidential primary" was "absurd, because Joe Biden has served this country honorably -- he's been a Democrat his entire life," said senior Biden adviser Symone Sanders, baking in an implicit jab at Warren's decision, in 1996, to switch her registration from Republican to Democrat.

"This has been and is about health care, and we want to be able to have a high-level policy conversation," Sanders said. "And as Democrats, we should be able to disagree without asserting that someone doesn't know what they're talking about or should be kicked out of the party or is corrupt."

The Warren campaign, which has made it a practice from the starting line not to swat at every provocation, opted against putting out a direct reply to Biden's initial criticism. Instead, her team amplified some of the ambient online criticism and appeared poised, at least until Friday afternoon, to leave it at that.

Despite the more forward wording, Warren's email offered a different flavor of the same message she regularly delivers to supporters on the campaign trail. Lines in the email detailing her anger "on behalf of everyone who is hurt by Trump's government, our rigged economy, and business as usual," were nearly indistinguishable from her stump speech.

Her frustration, Warren has said throughout the campaign, does not hold some distorting grip on her politics.

"I don't propose a wealth tax because I'm cranky," she said during a rally in Seattle this summer, a line she often repeats now on the stump, sometimes smiling broadly for effect. "I don't propose it because I'm mad at anybody."

This is the narrow line Warren has been made to walk throughout the campaign. Polling over the course of the past 10 months suggests she has successfully charted the path. Warren tops a number of early-state polls and is regularly found to be among the leaders when voters are asked to name their second-choice candidates.

'A smarty britches'

Still, the prospect of a Warren presidency has provoked anxiety and attacks from those opposed to her politics, and, quite literally, brought at least one grown man to the brink of tears.

"I don't need Elizabeth Warren, or the government, giving away my money," billionaire former hedge fund manager Leon Cooperman told CNBC earlier this week, his eyes watering, when the conversation turned to Warren's signature wealth tax.

Cooperman is one in a growing crowd of powerful men -- including some campaign rivals -- to paint Warren, who has campaigned on a populist promise to tax the rich in order to fund an ambitious suite of social programs, as angry or vindictive.

Asked this week if he would ever discuss tax policy with Warren, Microsoft co-founder Bill Gates said: "I'm not sure how open-minded she is ... or that she'd even be willing to sit down with somebody who has large amounts of money."

Before he bowed out of the race, former Rep. Beto O'Rourke of Texas suggested that Warren "is more focused on being punitive and pitting some part of the country against the other" than "lifting people up."

A source close to Biden's campaign described the new tone of attacks on Warren coming from him and his team as intentional in a different way: to communicate the message that "Warren is a smarty britches who thinks if you don't agree with her, you're an idiot."

Faced with accusations, amplified on social media by Warren's campaign during the week, over what some saw as sexist attacks, Biden's campaign also pointed to examples of him using the same words and phrases to criticize men -- including the time he called John McCain an "angry man" and "a little more angry than he usually is" in 2008, before labeling Mitt Romney an "elitist" in 2012.

Carol Moseley Braun, a Biden-supporting former senator from Illinois, said she's known the former vice president since the 1990s and has seen "nothing, zero, zippo, to suggest this man has got a sexist bone in his body. I just haven't."

"I don't think it's so much gendered criticism as it is a stupid argument, and you can quote me on that," she said. "It's a silly argument, as far as I'm concerned. The fact is that Sen. Warren is entitled to her position, VP Biden is entitled to his position and they're not going to be the same position -- they're different candidates."

She also alluded to Biden's implicit digs at Warren for being a registered Republican until the 1990s.

"To have somebody that just came around beating up on (Biden), to me, is just insulting," she said.

Biden's campaign also needled the Warren campaign for its response to his comments -- which during the week largely came through retweeting women and progressive activists who were critical.

"Donald Trump has already tried to extort a foreign country into intervening in this election, and we fought back. In his attempts to get reelected, no dirty trick will be off limits and no stone left unturned," said spokesman Andrew Bates. "Anyone who thinks they will be able to simply subtweet their way to victory against Donald Trump is flat-out wrong."