WASHINGTON — The U.S. Sentencing Commission voted unanimously Tuesday to allow some 19,500 federal prison inmates, most of them black, to seek reductions in their crack cocaine sentences.

The commission, which sets guidelines for federal prison sentences, decided to make retroactive its recent easing of recommended sentences for crack offenses.

Roughly 3,800 inmates could be eligible for release from prison within a year after the March 3 effective date of Tuesday's decision. Federal judges will have the final say whether to reduce sentences.

This will affect only about 15 offenders with cases from Utah, according to the U.S. Attorney's Office, because the state has one of the lowest numbers of crack cocaine cases in the nation.

The commissioners said the delay would give judges and prison officials time to deal with public safety and other issues.

U.S. District Judge William Sessions of Vermont, a commission member, said the vote on retroactivity will have the "most dramatic impact on African-American families." A failure to act "may be taken by some as particularly unjust," Sessions said before the vote.

Inmate family representatives and other advocates had said a Supreme Court decision on Monday could only improve chances the commission would address the long-criticized disparity in sentences for crack and powder cocaine offenses. Crack is predominantly used by blacks; powder cocaine, predominantly by whites.

In two decisions Monday, the Supreme Court upheld judges who rejected federal sentencing guidelines as too harsh and imposed more lenient prison terms, including one for crack offenses.

The administration restated its opposition to the easing on Tuesday, before the commission voted.