Posted by
CNN's Gregory Wallace

(CNN) - U.S. Rep. Paul Ryan urged his party to advance a forward-looking vision in his first high-profile speech since his failed bid for the White House alongside Mitt Romney.

The Wisconsin Republican also acknowledged that that he and Sen. Marco Rubio of Florida, who would speak at the dinner and receive an award, are seen as 2016 presidential contenders themselves.

"Know any good diners in Iowa or New Hampshire?" he asked Rubio at the beginning of his remarks. "I'm sure the press won't read too much into that."

In his remarks, Rubio replied, "I will not stand by and let the people of South Carolina be ignored."

At the Jack Kemp Foundation's award dinner, Ryan encouraged his party to find a "vision for bringing opportunity into every life - one that promotes strong families, secure livelihoods and an equal chance for every American to fulfill their highest aspirations for themselves and their children." That vision, he said, includes roles for government, private groups and free enterprise.

As he did in post-election interviews with local television stations, the former vice presidential candidate stood by the race he and Romney ran.

"Though I wish this election had turned out differently, I'm proud of the campaign Mitt Romney and I ran. He would have been a great president, and it would have been an honor to serve this country at his side," Ryan said.

"We gave this race our all, and I'm grateful for the nomination. It's thrilling when your team trusts you with the ball, and it's humbling when you advance the ball as far as you can, only to come up a little short."

He noted that President Barack Obama was returning to the White House facing "a stagnant economy and a fiscal mess." Obama has said he inherited some economic problems from his predecessor, President George W. Bush, and Ryan joked, "You might even say he'll inherit these problems."

Pointing to the Republicans' retention of their majority in the U.S. House, where he was re-elected, Ryan called on his party not to "spend the next four years on the sidelines."

But he also could be seen as distancing himself from some of Romney's controversial comments, in particular, that Obama had won by offering "gifts" to certain groups, and that 47% of voters were predisposed to vote against his candidacy. Both comments, made in private conversations with donors, drew criticism.

"Both parties tend to divide Americans into 'our voters' and 'their voters,' " Ryan said. "But Republicans must steer far clear of that trap. We must speak to the aspirations and anxieties of every American. I believe we can turn the engines of upward mobility back on, so that no one is left out from the promise of America. But it's going to require a bold departure from the approach that government has taken for the last five decades."

Ryan received the foundation's leadership award last year, and Rubio is the 2012 recipient. The award honors the late conservative congressman, cabinet secretary and GOP vice presidential nominee.

– CNN Political Editor Paul Steinhauser contributed to this report

Ryan encourages GOP to focus on the future in first major post-election speech