WASHINGTON — The U.S. Sentencing Commission voted unanimously yesterday 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. Most of those eligible could receive no more than a two-year cut in their prison terms, but roughly 3,800 inmates could be released from prison within a year after the March 3 effective date of yesterday’s decision. Federal judges will have the final say whether to reduce sentences.

The commissioners said the delay until March would give judges and prison officials time to deal with public safety and other issues. The commission took note of objections raised by the Bush administration, but it said there is no basis to treat convicts sentenced before the guidelines were changed differently from those sentenced after the changes.

The sentencing commission recently changed the guidelines to reduce the disparity in prison time for the two crimes. The new guidelines took effect November 1.

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,” Judge Sessions said before the vote.