(CNN) A fight for the moral high ground is publicly playing out over the US Women's National Team's gender discrimination lawsuit against the US Soccer Federation.

While both sides have agreed to mediation, US Soccer is now posting numbers saying the back-to-back FIFA Women's World Cup champions actually earn more than the US Men's National Team.

It's a claim the women say is "utterly false." The women also received the backing of the men's team, which issued a statement saying they support the women "in their pursuit of fair compensation for their work as professional soccer players."

On Monday, US Soccer president Carlos Cordeiro released an open letter on Twitter, saying that from 2010 through 2018 the federation paid $34.1 million in salary and game bonuses to the women, compared to $26.4 million for the men.

Those figures do not include benefits, such as healthcare, that the women receive. Included in the federation's numbers is that US Soccer pays WNT contracted players a salary to play in the National Women's Soccer League, while the men are paid by their individual teams.

The women's and men's compensation structures are different, as those each were collectively bargained.

And the fact sheet... (2/2) pic.twitter.com/XFofHS90f1 — Carlos Cordeiro (@CACSoccer) July 29, 2019

"In the weeks ahead, we'll focus on preparing for mediation and resolving this matter in the best interests of the WNT and US Soccer," Cordeiro said.

"I want you to know that US Soccer is committed to doing right by our players, and I've been encouraged by the public comments from players expressing their desire for a cooperative approach. I remain optimistic that we can find common ground.

"Together, I believe we can get this done."

Alex Morgan, Megan Rapinoe, and Allie Long celebrate during the U.S. Women's National Soccer Team Victory Parade and City Hall Ceremony on July 10, 2019 in New York City.

'Utterly false'

In a written statement, a spokesperson for the USWNT players says the figures are misleading.

"This is a sad attempt by USSF to quell the overwhelming tide of support the USWNT has received from everyone from fans to sponsors to the United States Congress," Molly Levinson said in a statement.

"The USSF has repeatedly admitted that it does not pay the women equally and that it does not believe the women even deserve to be paid equally. This is why they use words like 'fair and equitable,' not equal in describing pay.

"The numbers USSF uses are utterly false and, among other things, inappropriately include the NWSL salaries of the players to inflate the women's players compensation. Any apples to apples comparison shows that the men earn far more than the women.

"In the most recent CBA negotiation, USSF proposed a compensation structure that is exactly the same as the MNT's compensation structure but with less compensation across the board. In every instance, win or draw for a friendly or competitive match, the women players were offered less compensation. Equal Pay was never on the table for the women regardless of structure.

"The USSF fact sheet is not a 'clarification.' It is a ruse.

"Here is what they cannot deny. For every game a man plays on the MNT he makes a higher base salary payment than a woman on the WNT. For every comparable win or tie, his bonus is higher.

"That is the very definition of gender discrimination. For the USSF to believe otherwise, is disheartening but it only increases our determination to obtain true equal pay. If the USSF cannot agree to this at the upcoming mediation, we will see them in the court of law and the court of public opinion."

The US Men's National Team said they too "were not impressed" by Cordeiro's letter. "The women's national team players deserve equal pay and are right to pursue a legal remedy from the courts or Congress," the men's team said.

Rose Lavelle of the USWNT celebrates with Emily Sonnett after winning Women's World Cup final.

Victory tour

In March, members of the USWNT filed a federal class-action lawsuit against US Soccer, citing gender discrimination.

The suit alleges that the federation discriminates by paying the women less than members of the men's national team "for substantially equal work and by denying them at least equal playing, training, and travel conditions; equal promotion of their games; equal support and development for their games; and other terms and conditions of employment equal to the MNT."

Overall, the American women have had much more success on the pitch than their male counterparts, winning four World Cups and four Olympic gold medals.

During that time frame US Soccer provided in Monday's letter, the women have won two World Cups, in 2015 and earlier this month, while the men missed the 2018 World Cup, having failed to qualify.

The USWNT begins its World Cup victory tour on Saturday with a match against Ireland at the Rose Bowl in Pasadena, California.