“There was no intent,” the American basketball star told a Russian judge, as any resolution of the highly politicized case appeared to shift toward the diplomatic arena.

Courts in Russia heavily favor the prosecution, experts said, pointing to a prisoner swap as perhaps the W.N.B.A. star’s best chance to come home.

The campaign by dozens of organizations representing people of color, women and L.G.B.T.Q. voters comes amid growing frustrations over the pace of the U.S. effort to bring her home.