Morgan and Rapinoe are among 28 members of the US women's national squad who on Friday filed a federal lawsuit in Los Angeles alleging gender discrimination by the United States Soccer Federation (USSF)
The lawsuit said the USSF had "utterly failed to promote gender equality" between the women's team and far less successful men's national team.
The legal fight was launched just three months before the US women defend their crown at the World Cup in France.
However on Monday, Morgan said there was no chance that the women's team would boycott the tournament in an attempt to further their cause.
"I don't think it's ever been in our minds to step off the field," Morgan told ABC network's Good Morning America program.
"We've been looking forward to the World Cup for three years now. We want to continue to play for our country at the highest stage this summer in France."
US teams have taken the Women's World Cup title three times, including the inaugural 1991 edition in China, the 1999 event on home soil and in Canada four years ago.
US men, by comparison, were third in 1930 in the first World Cup but their best showing since was a quarter-finals loss in 2002.
US women players seek millions of dollars in back pay and damages and have long argued the inequalities compared to men include quality of venues, number of matches, medical treatment, coaching and training opportunities and transportation.
Issues include when US women called off a 2015 match in Honolulu on articifical turf due to safety worries over poor field conditions.
Rapinoe told ABC television on Monday the team was confident of victory.
"We know in our hearts, and we know with the facts that we have, that we're on the right side of this," Rapinoe said.
"I don't think anyone can argue that there's gender inequities in this world, that there's a pay gap, that there's pay discrepancies."
Rapinoe said she hoped the stance of the US women would send a message to women everywhere.
"The big picture ultimately is just giving that message that you should fight for what you believe in," she said. "You should fight for what you feel you earn and never give up."