The US beat the Netherlands in the final to win the World Cup for a fourth time in 2019
The US Soccer Federation has offered identical contracts to its men's and women's national teams in an attempt to resolve its gender pay dispute.
In May 2020, a lawsuit from the women's team for equal pay was dismissed by a judge, with an appeal pending.
The USSF says a single equal pay structure is "the best path forward".
In a strongly worded tweet, the United States Women's National Team Players Association (USWNTPA) described the proposal as a "PR stunt".
USSF has called on players and their unions for support in helping to "equalise" World Cup prize money, which is at the root of the teams' pay gap.
But a statement on the USWNTPA Twitter account questioned the offer, stating: "USSF's PR stunts and bargaining through the media will not bring us any closer to a fair agreement.
"In contrast, we are committed to bargaining in good faith to achieve equal pay and the safest working conditions possible.
"The proposal that USSF made recently to us does neither."
In reply, the USSF dismissed the USWNTPA's criticism of the proposal, stating: "An offer on paper of identical contracts to the USWNT and USMNT, and to discuss equalizing prize money, is real, authentic and in good faith.
"A publicity stunt is a 90-minute one-sided movie."
President Cindy Parlow Cone said in an open letter on 10 September that "the massive discrepancy" in World Cup prize money is "by far the most challenging issue" in the negotiations with the teams.
"Until Fifa equalises the prize money that it awards to the men's and women's World Cup participants, it is incumbent upon us to collectively find a solution," she said.
The USSF has previously said women's World Cup bonuses cannot match those of the men because of huge differences in payments made to federations by Fifa for men's and women's tournaments.
"US Soccer will not agree to any collective bargaining agreement that does not take the important step of equalising Fifa World Cup prize money," a USSF statement said.
Women's World Cup: What is the pay gap?
The United States won the Women's World Cup for the fourth time in France in 2019 and have claimed Olympic gold five times. The men's team failed to qualify for the 2018 World Cup in Russia.
Prize money at the 2018 men's World Cup totalled $400m (£312m), with winners France receiving $38m (£29.7m). The prize fund for the 2019 Women's World Cup was $30m (£23.4m), with winners the United States receiving $4m (£3.1m).
The lawsuit from the women's team was filed by 28 women's national team players seeking $66m (£52.8m) in damages under the Equal Pay Act.
"This proposal will provide a revenue sharing structure that would allow all parties to begin anew and share collectively in the opportunity that combined investment in the future of US Soccer will deliver over the course of a new collective bargaining agreement," the USSF statement added.
The men's and women's unions are separate and have no obligation to bargain jointly or agree similar terms under US law.
If either party does not agree to a new deal, US Soccer says it will invite each union to sit in on negotiations for full transparency.
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