Aug 7 (Reuters) - U.S. President Donald Trump is moving forward with his attempt to fire Federal Reserve Governor Lisa Cook after the U.S. Supreme Court in June refused to let the president fire her, ABC News reported on Friday, citing sources.

The White House told Cook in a letter this week that the president was "considering" removing her from her role and demanded she respond to unproven mortgage fraud allegations within three weeks, ABC reported.

Cook and the Federal Reserve did not immediately respond to requests for comment.

Trump last year cited mortgage fraud in trying to fire Cook, the first Black woman to serve as a Fed governor. Cook denied the allegations, calling them a pretext to remove her for monetary policy differences.

The U.S. Supreme Court refused in June to allow the firing, standing firm to preserve the central bank's cherished independence against the Republican president's unprecedented challenge.

The court, in a 5-4 ruling, blocked Trump from removing Cook for now, providing a safeguard for the Fed specifically.