WASHINGTON—The Justice Department said Friday its prosecutors won't pursue criminal charges against their boss, Attorney General Eric Holder, over his refusal to turn over documents sought by House Republicans.

The move was an expected response to a vote in the Republican-controlled House Thursday citing Mr. Holder with contempt of Congress. Under the law, it is the responsibility of the U.S. attorney for the District of Columbia to enforce the House contempt finding, including pursuing a criminal prosecution before a grand jury.

The vote came in a dispute over documents related to the botched Fast and Furious gun-trafficking probe, in which federal agents allowed suspected smugglers to buy about 2,000 firearms, many of which were smuggled to Mexico.

President Barack Obama this month asserted executive privilege to block the release of Justice Department documents that Republican House lawmakers have subpoenaed. Mr. Holder had earlier refused to release the documents.

Deputy Attorney General James Cole notified House Speaker John Boehner that the department would rely on internal precedent dating back to the Reagan administration to ignore the House contempt citation.