Christie, repeatedly applauded for his remarks, appeared at the event after Thursday's release of a report he commissioned that cleared him of wrongdoing in the George Washington Bridge lane closures.
The report, which also dismissed allegations that Christie officials threatened to withhold Hurricane Sandy aid from the mayor of Hoboken, has prompted skepticism about its impartiality and conclusions, which were reached without interviewing key players in the bridge scandal.
Since the report was released, Christie has given national television interviews and held his first news conference in months. Last week, he said he had not ruled out running for president.
In Las Vegas, he briefly addressed the bridge controversy, describing it as a lesson not to place too much trust in aides.
"It is always confidence-shaking and disappointing when people you trust let you down," he said.
Instead, Christie focused on the Republican Party's future.
"I assume, as Republicans, you might be interested once again in winning elections," he said. "I am not in this business to have an academic conversation."
Citing his election victories in a state he said was so blue "we haven't elected a Republican to the U.S. Senate in 42 years," Christie said the GOP needed to do a better job of reaching out to minority voters.
Many in minority communities "are not used to being listened to by our party," he said. "Leadership can come from listening."
Attacking President Obama, Christie said the United States was perceived as weaker today than five years ago.
"We need to start with strong, decisive leadership at the top who understands every signal you send as a leader is interpreted," he said.
He also expressed familiar criticism of the "dysfunction" of Washington, which he argued had diminished America's image abroad: "We no longer have a government that people want to emulate."
Saying America's allies needed to be sure of its support - and its enemies of its opposition - Christie cited his leadership style.
"In New Jersey, no one has to wonder whether I'm for them or against them," he said. "There is never really a cloud of indecision around what I say and what I do."
Christie, who took questions afterward, shot down a question asking his position on sharia law, calling it "Internet blog B.S." stemming from his decision to appoint a Muslim Superior Court judge.
"It's ridiculous and insulting . . . that people somehow believe that means I'm for sharia law. It's crap," he said.
Also speaking Saturday were Wisconsin Gov. Scott Walker and Ohio Gov. John Kasich.
The governors - also considered possible presidential contenders in 2016 - talked more about their home-state records than foreign policy, with Walker making pitches similar to Christie's.
Walker described battling unions and teacher-tenure rules - familiar material for Christie - and winning over Hispanic voters as a county executive.
Michael Miller, a physician from Cleveland, said Christie had "a little bit more presence."
"There's something warm about Gov. Christie," Miller said. He said he appreciated Christie's message that the party needed to listen to constituencies that hadn't traditionally lent their support: "It's a different view for the Republicans to not just talk in the negative."
Christie took some heat Saturday for using the phrase occupied territories while recounting his 2012 trip to Israel.
Morton Klein, national president of the Zionist Organization of America, said Christie should have used the term disputed territories.
Klein said that after the speech, he approached Christie, who "refused to acknowledge" what Klein considered an error.
"I'm shocked he would use the term in front of a pro-Israeli, Jewish group," Klein said.
Matt Brooks, executive director of the Republican Jewish Coalition, called the term a "slip of the tongue."
"He was not trying to make a declaration of policy," Brooks said.