Rudy: "You don't always win, but you can always try to do it right."

"It's not over until it's over," a woman yells to Rudy Giuliani from his election night audience ...

But it appears it is.

The former mayor congratulated his opponents on a hard-fought campaign. "They are truly all honorable people, honorable men who are fighting what they believe in," he said. "Our party will be stronger as a result of the competition that we are going through."

Speaking in the past tense about his bid, but not offering yet that he would exit, Giuliani said "winners dream of a better future and then they help to bring it into reality." But added, "the responsibility of leadership doesn't end in a single campaign, if you believe in a cause it goes on, and you continue to fight for it and we will."

Giuliani said he is proud that his campaign stayed "positive" and ran "a campaign of ideas."

"We ran a campaign that was uplifting," he said. "You don't always win, but you can always try to do it right and you did. That's what the American people deserve."

He went on to advocate for strength in the fight to preserve our national security and our economy. He pushed for school choice as well. And he said the GOP -- the party of Abe Lincoln and Ronald Reagan and George Bush -- must be the party of freedom.

"The best way to achieve peace is through overwhelming strength," he said.

(JENNIFER SKALKA)