WASHINGTON — Joe Walsh, the conservative radio show host and former Republican lawmaker from Illinois who rode the 2010 Tea Party wave to serve one term in Congress, announced on Sunday that he is running for president, challenging President Trump for the Republican nomination.

Mr. Walsh announced his candidacy in an interview with George Stephanopoulos on ABC’s “This Week,” while Mr. Trump was in Biarritz, France, for the G7, where he admitted he had “second thoughts” about ratcheting up tariffs and threats against China last week — moves that rattled global stock markets — before his spokeswoman said his statement was being misinterpreted.

“We’ve got a guy in the White House who is unfit, completely unfit, to be president and it stuns me that nobody stepped up,” Mr. Walsh said in announcing his candidacy, claiming that “everyone” in the Republican Party believes Mr. Trump is not fit for the job.

Mr. Walsh’s decision to announce his candidacy on television, aides said, is a preview of a television-centric strategy designed to rattle a television-focused president with a rare challenge from within the party. Mr. Walsh, a former supporter and acerbic Clinton critic, in 2016 wrote on Twitter: “On November 9th, if Trump loses, I’m grabbing my musket. You in?”