The U.S. men’s soccer team players association, in the midst of negotiations with the U.S. Soccer Federation over a new collective-bargaining agreement, on Wednesday called on the federation to pay the U.S. women’s team “significantly more” than the men were paid under their recently expired deal.

The men’s players association’s position, outlined in a nearly-1,900-word news release, appears to have been prompted by what it says is the federation’s current negotiating position: that the U.S. men’s team’s compensation should...