WASHINGTON — Republicans are growing increasingly concerned that Donald J. Trump’s inflammatory language is damaging the party, fearing that his remarks are hardening the tone of other candidates on racial issues in ways that could repel the voters they need to take back the White House.

Some party leaders worry that the favorable response Mr. Trump has received from the Republican electorate is luring other candidates to adopt or echo his remarks. It is a pattern, they say, that could tarnish the party’s image among minority voters.

“Any candidate that allows Trump to dictate the conversation about what they’re campaigning on is going to be harmed irreparably,” said Josh Holmes, a Republican strategist and the architect of Senator Mitch McConnell’s re-election campaign in Kentucky last year. “And to the extent that there are mainstream candidates dragged into the musings of Trump on a day-to-day basis is really bad news for us.”

Since he entered the race in June with a declaration that Mexican immigrants were rapists and drug traffickers, Mr. Trump has given voice to conservative activists’ unease with America’s changing demography. But his attack last week on Jeb Bush for speaking Spanish on the campaign trail set off a new, more intense wave of anger from Republicans who say they believe that Mr. Trump’s widely covered provocations are becoming toxic for a party struggling to appeal to nonwhite voters.