MIAMI — Representative Allen B. West will leave Congress much as he arrived two years ago: combative, blunt and the standard-bearer for Tea Party supporters who urged him to shake up government.

After nearly two weeks of legal and electoral jousting, Mr. West, 51, conceded on Tuesday to his Democratic challenger in the Nov. 6 election, Patrick Murphy, a political newcomer from South Florida. Mr. Murphy, 29, won the race, in St. Lucie, Martin and northern Palm Beach Counties, by 1,904 ballots, or 0.58 percent of the vote.

“While a contest of the election results might have changed the vote totals, we do not have evidence that the outcome would change,” Mr. West said in a statement on Tuesday morning. “Given the extremely high evidentiary hurdles involved in a successful challenge, I will not ask my generous supporters to help fund a drawn-out, expensive legal effort with little chance of success.”

In an election season rife with bitter, expensive races across the nation, the contest between Mr. West, a retired Army lieutenant colonel and a prodigious fund-raiser, and Mr. Murphy, a construction company official, was among the fiercest and most expensive. The rivals ran explosive political advertisements calling into question each other’s moral character and exchanged cutting words on the campaign trail.