The high court acted in a one-line order without further comment.
Lawyers for a group seeking to intervene in the case had asked Justice Anthony Kennedy to postpone the judge’s ruling to allow more time for an appeal.
The group, the National Organization for Marriage (NOM), supports retaining the traditional definition of marriage of a union between one man and one woman.
Justice Kennedy requested briefs from Oregon officials and the same-sex couples who had filed the initial lawsuits. Oregon officials had ceased to defend the ban in the case before the federal court, calling the measure unconstitutional, and both the state and the couples urged the Supreme Court to reject the stay request.
“The application for stay presented to Justice Kennedy and by him referred to the Court is denied,” the order said in its entirety.
The action means that same-sex couples in Oregon can continue to apply for licenses, get married, and enjoy the full benefits of marriage in that state.
On May 19, US District Judge Michael McShane struck down a 2004 amendment to Oregon’s constitution that restricted marriage to one man and one woman.
He ruled that the measure violated the Equal Protection Clause of the 14th Amendment by degrading and demeaning the relationships of committed same-sex couples by refusing to allow them to marry.