WASHINGTON—A divided Supreme Court Monday upheld an Arizona tax-credit program that offers a dollar-for-dollar reduction of state income tax payments to organizations that support religious schools, opening the door to the expansion of such programs nationwide.

By a 5-4 vote, the justices ruled that Arizona taxpayers have no right to allege in court that the state's tax-credit program violates the First Amendment prohibition of government "establishment of religion." The decision upheld the program without addressing the allegation that it is unconstitutional, and effectively overruled decades of precedent permitting lawsuits against government programs that subsidize religious institutions through tax incentives.

The Arizona law doesn't bar discrimination on religious grounds, and the taxpayer plaintiffs alleged that many of the schools benefiting from the tax credit required adherence to a particular faith.

The ruling appears to clear a path for other states to offer similar tax breaks in response to advocates of giving parents disenchanted with public schools assistance to send their children to religious schools. Florida, Georgia, Indiana, Iowa, Pennsylvania and Rhode Island already have such measures on the books, and similar proposals are pending in at least 11 other states.

"Every state that is considering a tax-credit program can rest easy," said Robert Enlow, president of the Foundation for Educational Choice, a group which favors public subsidies for private schools.