Kari Lake, the Republican former news anchor who refused to acknowledge her loss in the Arizona governor’s race last year, filed paperwork on Tuesday to run for Senate, setting up what is expected to be one of the most competitive Senate races in the country as Republicans try to win back the chamber.
The incumbent, Senator Kyrsten Sinema, who left the Democratic Party last year to become an independent, has not confirmed whether she will run for re-election, but a prominent Democrat, Representative Ruben Gallego, is already challenging her.
Mark Lamb, a right-wing sheriff and an ally of former President Donald J. Trump, is also running.
On Tuesday, Ms. Lake was in Washington, where she met with several Republican members of the Senate, including John Cornyn of Texas and Ron Johnson of Wisconsin, according to people familiar with the discussions who insisted on anonymity because they were not authorized to discuss private conversations.
She also met with Senator Steve Daines of Montana, the chairman of the National Republican Senatorial Committee. Mr. Daines is considering an endorsement for Ms. Lake, which may convince moderate donors to give the conservative firebrand a second look.
A person close to Ms. Lake confirmed that she had filed paperwork to open her Senate campaign. She is scheduled to hold her first rally as a candidate next week.
Ms. Lake lost the governor’s race to Katie Hobbs by about 17,000 votes, a little over half a percentage point. She was one of many Republicans, including several in Arizona, who lost close contests last year after running on Mr. Trump’s lie that the 2020 election had been stolen. While most of those Republicans conceded their own losses, Ms. Lake followed Mr. Trump’s lead and continued to insist that she had won even after her legal challenges were rejected.
Her campaign circulated testimonials from supporters who claimed to have been disenfranchised by technical problems with voting machines, but a New York Times review found that most of them had been able to vote. She filed a lawsuit in December alleging deliberate misconduct by election officials — though she did not provide evidence of that, or of any unintentional disenfranchisement. A judge rejected her claims later that month.
In February, when she said she was considering running for Senate, she was still claiming to be the rightful governor and raising money for lawsuits. The Arizona Supreme Court refused to hear her case in March, and in May, a lower-court judge threw out a challenge she had filed over the verification of signatures for mail-in ballots.
During her campaign, she followed Mr. Trump in both style and substance, using the news media as a foil after working for years as a local television anchor in Phoenix. She repeatedly promoted Mr. Trump’s election lies, won his endorsement and in the Republican primary, defeated Karrin Taylor Robson, a rival supported by the state’s G.O.P. establishment.