United States women's national team co-captain Megan Rapinoe says players have not closed the door on resolving their equal pay dispute with U.S. Soccer out of court, but any conversations with the federation must begin with women's players receiving equal pay to their male counterparts.

Rapinoe and teammate Christen Press appeared on ABC's "Good Morning America" and NBC's "Today" on Thursday, a day after mediation between the U.S. Soccer Federation and the 28 members of the women's team who filed a gender discrimination suit in March reached an impasse. Both sides issued strongly worded statements of frustration following the breakdown.

"We're always open to hearing that conversation if they're ready to have it," Rapinoe said on NBC. "That's the only federation we can play for. We're the only team that they have. ... So we're sort of tethered together in that way. But at any point if they want to have a serious conversation and are willing to not only talk about paying us equally and valuing us in that way, but actually doing it and showing us that they'll do it, our ears are always open.

"I don't think anybody wants to go to litigation. But with that said, we're very confident in our case."

A letter dated Aug. 12 -- signed by all 28 players involved in the lawsuit and sent to U.S. Soccer officials as mediation began -- outlined optimism for a resolution, but Press said Thursday that the two sides never progressed past the primary philosophical difference.

"I think, unfortunately, it was just the concept of paying us equally," Press said of where mediation broke down. "We never even got past that. We were very hopeful in our discussions with them that they were going to take our proposals and our positions seriously, which is simply that every game that we play, we get compensated the same way a man would for playing or winning that game. And it broke down right there."

Rapinoe and Press reiterated throughout their appearances on the morning television shows that players seek full equality of pay.

"When we play a game and we win that game -- or we tie that game or we lose that game -- that we should be paid the same as our male counterparts," Rapinoe said on NBC. "I don't think that that's an unrealistic or unreasonable ask to have equality."

Most recently in an open letter from president Carlos Cordeiro released on July 29, U.S. Soccer has long used the word "fairly" rather than "equally" as the baseline of its position on pay.

Complicating the issue is that the men's and women's teams operate with separate collective bargaining agreements and separate pay structures. Rapinoe acknowledged Thursday the "realities are different" for the two teams, but she insisted there is little flexibility.

"This isn't bargaining," Rapinoe said.

Both sides voiced frustration at Wednesday's impasse.

"We always know there is more we can do," U.S. Soccer said in its statement after mediation broke down. "We value our players and have continually shown that, by providing them with compensation and support that exceeds any other women's team in the world."

No new mediation is currently scheduled to prevent the dispute from reaching a federal court. The dispute is therefore unlikely to be resolved before the U.S. begins preparations for the 2020 Olympics.

U.S. Soccer named former World Cup winner Kate Markgraf as its first general manager for the women's national team. Markgraf will run the search for a coach to replace Jill Ellis, who will step down at the conclusion of the team's current Victory Tour. The new coach will then have to prepare the team for Olympic qualifying, likely in January or February of next year.

Press offered no hint Thursday that players would look to use Olympic participation as leverage and said past results -- with the World Cup the most recent example -- demonstrated their ability to separate off-field issues from on-field performance.

"I think that we've shown that we're able to do a lot of work off the field and still have successful results," Press said. "This has been going on -- this fight actually has been going on forever. I think being part of being on the women's national team means that you're taking part in this torch-carrying for women. And we take a lot of pride in that, and it gives us a great purpose."