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Mr Schiff said that Mr Biden "has been one of the most consequential presidents in our nation's history", and he could "secure his legacy of leadership" by allowing Democrats to support another candidate.
"Our nation is at a crossroads. A second Trump presidency will undermine the very foundation of our democracy, and I have serious concerns about whether the President can defeat Donald Trump in November," he added.
Mr Biden has repeatedly said he intends to stay in the race, despite the calls for him to step aside.