KBR said in a statement Monday that it withdrew the appeal to not risk violating a recently passed federal provision it called "very broad and vague," that with companies that prohibit employees from seeking redress for certain crimes through the courts.
"As a result, KBR did not want to risk being in violation of the amendment, so the company withdrew its petition," KBR said in a statement.
Diana Gabriel, a spokeswoman for Halliburton, also confirmed the appeal was withdrawn but declined to elaborate.
Jamie Leigh Jones, of Texas, sued the companies after she says she was raped while working for KBR in Baghdad in 2005. KBR and Halliburton split in 2007.
The companies argued that Jones' contract required claims against them be settled through arbitration.
But the 5th U.S. Circuit Court of Appeals in New Orleans sided with Jones in September, saying her case could go to trial.
A trial date has been set for May 2011, Jones' attorney Todd Kelly said.
Now that the Supreme Court appeal has been withdrawn, "it looks like we're headed for trial," said Kelly, who is based in Houston.
The Associated Press usually doesn't name people alleging sexual assault, but Jones' identity has been broadcast in media reports and on her own Web site.
No one has been charged in Jones' case or in any other alleged sexual assaults on women who did civilian work in Iraq. At least three women have testified before Congress about while working as military contractors in Iraq.
More on Iraq Rape Case
Senate OKs Measure Related to Rape Claim
Another Iraq Contractor Worker Claims Rape
More Women Claim Sex Abuse At KBR
Clinton Joins Call For Iraq Rape Probe
Halliburton Under Fire Over Rape Charge