WASHINGTON — President Donald Trump on Friday ordered a committee of inquiry to investigate whether Federal Reserve Governor Lisa Cook made false statements connected to one or more mortgage documents, escalating his campaign to remove her from the central bank. In a presidential memo, Trump said the inquiry would examine the allegations and argued that he must be able to dismiss officials he believes cannot be trusted to follow the law. The allegations have not been established by the inquiry. Trump has previously sought to oust Cook as part of a broader push to influence the Federal Reserve, including pressure for lower interest rates. The Supreme Court blocked his earlier effort to remove her, ruling that the administration had not afforded Cook due process. The inquiry comes amid other efforts to scrutinize the Federal Reserve. Last week, the central bank’s inspector general found no basis for the Justice Department to reopen a criminal investigation into renovations at the Fed’s headquarters. That investigation had been viewed as a possible avenue for removing former Chair Jerome Powell from his seat on the board. The Federal Reserve sets U.S. monetary policy, including benchmark interest rates that affect borrowing costs across the economy. The dispute over Cook’s position raises questions about the limits of presidential authority over the institution and its independence from political pressure.