Call it the Oval Office virus. After less than a month in office, President Donald J. Trump, who as a candidate embraced WikiLeaks and a torrent of leaks about his rival Hillary Clinton’s campaign, has become a champion of government secrecy. In a rowdy, 77-minute press conference Thursday, Trump said that he had personally instructed the Justice Department to open a criminal investigation into the leak of embarrassing information about his conversations with foreign leaders and former National Security Adviser Michael T. Flynn’s contacts with Russia. While it is unusual for a president to ask for such a criminal investigation, or to discuss it publicly, no law prevents him from doing so. “It could be perceived as a political witch hunt,” warned Susan Hennessey, a scholar at the Brookings Institution and former intelligence agency lawyer.