WASHINGTON (Reuters) - U.S. Republican presidential candidate Donald Trump shot back at President Barack Obama's criticism of him as unfit for office, saying Democratic rival Hillary Clinton has embraced policies that have hurt national security and America's workers.

"Hillary Clinton has proven herself unfit to serve in any government office," Trump said in a statement shortly after Obama issued a scathing attack and challenged Republican leaders to withdraw support for their "woefully unprepared" nominee.

(Reporting by Susan Heavey; Editing by Doina Chiacu)