WASHINGTON — President Trump’s embrace of the country’s racially charged past has thrown the Republican Party into crisis, dividing his core supporters who have urged him on from the political leaders who fear that he is leading them down a perilous and shortsighted path.

The divisions played out in the starkly different responses across the party after Mr. Trump insisted that left-wing counterprotesters were as culpable as neo-Nazis and white supremacists for the bloodshed in Charlottesville, Va., over the weekend. Much of the right was ecstatic as they watched their president fume against the “violent” left and declare that “very fine people” were being besmirched for their involvement in the demonstration.

Stephen K. Bannon, the president’s chief strategist, said in an interview that if Democrats want to fight over Confederate monuments and attack Mr. Trump as a bigot, that was a fight the president would win.

“President Trump, by asking, ‘Where does this all end’ — Washington, Jefferson, Lincoln — connects with the American people about their history, culture and traditions,” he said.