WASHINGTON — The U.S. Defense Department will appeal a military judge’s ruling that plea agreements struck by Khalid Sheikh Mohammed, the alleged mastermind of the September 11, 2001, attacks, and two of his co-defendants are valid, a defense official said Saturday. The ruling this past week voided Defense Secretary Lloyd Austin’s order to throw out the deals and concluded that the plea agreements were valid. The judge granted the three motions to enter guilty pleas and said he would schedule them for a future date to be determined by the military commission. The department will also seek a postponement of any hearing on the pleas, according to the official, who was not authorized to publicly discuss legal matters and spoke on condition of anonymity. Rear Admiral Aaron Rugh, the chief prosecutor, sent a letter Friday to the families of 9/11 victims informing them of the decision. The ruling by the judge, Air Force Colonel Matthew McCall, allowed the three 9/11 defendants to enter guilty pleas in the U.S. military courtroom at Guantanamo Bay, Cuba, and would spare them the risk of the death penalty. The pleas by Mohammed, Walid bin Attash and Mustafa al-Hawsawi would be a key step toward closing out the long-running and legally troubled government prosecution in the attacks that killed nearly 3,000 people. Government prosecutors had negotiated the deals with defense lawyers under government auspices, and the top official for the military commission at Guantanamo had approved the agreements. But the deals were immediately slammed by Republican lawmakers and others when they were made public this summer. Within days, Austin issued an order saying he was nullifying them. He said plea bargains in possible death penalty cases tied to one of the gravest crimes ever carried out on U.S. soil were a momentous step that should only be decided by the defense secretary. The judge had ruled that Austin lacked the legal authority to toss out the plea deals. The agreements, and Austin’s attempt to reverse them, have made for one of the most fraught episodes in a U.S. prosecution marked by delays and legal difficulties. That includes years of ongoing pretrial hearings to determine the admissibility of statements by the defendants, given their torture in CIA custody. While families of some of the victims and others are adamant that the 9/11 prosecutions continue until trial and possible death sentences, legal experts say it is not clear that could ever happen. If the 9/11 cases ever clear the hurdles of trial, verdicts and sentencings, the U.S. Court of Appeals for the District of Columbia Circuit would likely hear many of the issues in the course of any death penalty appeals. The issues include the CIA destruction of videos of interrogations, whether Austin’s plea deal reversal constituted unlawful interference and whether the torture of the men tainted subsequent interrogations by “clean teams” of FBI agents that did not involve violence.