His announcement Tuesday leaves a virtually clear path to the Republican nomination for Linda McMahon, former chief executive officer of World Wrestling Entertainment, and an anticipated brutal fight with Attorney General Richard Blumenthal, the democratic nominee, in November, The New York Times reported.
Simmons, who announced his candidacy 16 months ago, grabbed the early lead in polling, but steadily lost momentum. The state Republicans' endorsing convention last week backed McMahon.
After announcing he would challenge McMahon on the Aug. 10 primary ballot, Simmons was under pressure to abandon his bid by party leaders concerned that intra-party fighting would hurt the GOP's chances of claiming the seat of retiring Sen. Christopher Dodd in the fall, the Times said.
Simmons cited as a reason for his departure a huge financial advantage enjoyed by McMahon, who said she was ready to spend up to $50 million of her own money to win the seat.
"We understand the mathematical reality of competing against an opponent with unlimited financial resources," he said. "This is not an easy decision or a happy decision. But we believe it is the right decision."
Simmons said he would keep his name on the Republican primary ballot in August. He did not endorse McMahon or GOP hopeful Peter Schiff, who is drawing some support from the Tea Party movement.
Blumenthal has been under fire since the Times reported last week some of his comments about serving in Vietnam didn't square with the record. After the article was published, Blumenthal said he takes "full responsibility" for misleading statements about his military service in the Vietnam war.