Mr. Trump has also sought to block the release of records from the files of Mark Meadows, his former chief of staff; Stephen Miller, his former senior adviser; and Patrick F. Philbin, his former deputy counsel. Mr. Trump also sought to stop the release of the White House Daily Diary — a record of the president’s movements, phone calls, trips, briefings, meetings and activities — as well as logs showing phone calls to the president and to Vice President Mike Pence concerning Jan. 6.Finally, Mr. Trump tried to keep secret a draft proclamation honoring the Capitol Police and two officers who died after the riot, Brian D. Sicknick and Howard Liebengood, as well as related emails; a memo about a potential lawsuit against several states that Mr. Biden won; an email chain from a state official regarding election-related issues; and talking points on supposed election irregularities in one county in Michigan.Mr. Trump told the justices that he had a constitutional right to shield the materials from Congress even though Mr. Biden declined to invoke executive privilege over them.“The disagreement between an incumbent president and his predecessor from a rival political party,” Mr. Trump’s lawyers told the court, “is both novel and highlights the importance of executive privilege and the ability of presidents and their advisers to reliably make and receive full and frank advice, without concern that communications will be publicly released to meet a political objective.”Lawyers for the House committee responded that the Supreme Court should not thwart its inquiry. “The select committee’s work,” they wrote, “is of the highest importance and urgency: investigating one of the darkest episodes in our nation’s history, a deadly assault on the United States Capitol and Congress, and an unprecedented disruption of the peaceful transfer of power from one president to the next.”Justice Brett M. Kavanaugh, who served as staff secretary to President George W. Bush, was the only justice to issue a signed opinion in the case. He said the appeals court, in a passage the majority had said was nonbinding, had been wrong in its analysis.“A former president must be able to successfully invoke the presidential communications privilege for communications that occurred during his presidency, even if the current president does not support the privilege claim,” Justice Kavanaugh wrote. “Concluding otherwise would eviscerate the executive privilege for presidential communications.”