COLUMBUS, Ohio — Gov. John R. Kasich, a voluble and blunt-talking maverick who is hoping his upbeat vision for a united America can catapult him to the White House, declared Tuesday that he is running for president, telling a crowd here that he has “the experience and the testing — the testing which shapes you and prepares you for the most important job in the world.”

Mr. Kasich, joined by his wife and 15-year-old twin daughters, addressed several thousand cheering supporters inside the student union building at Ohio State University here, offering a centrist appeal designed to paint him as a common-sense Midwesterner who can fix a broken Washington. He avoided attacking President Obama, as his Republican rivals have done.

The event was a return of sorts: As an 18-year-old Ohio State freshman in 1970, Mr. Kasich wrote President Richard M. Nixon to plead, successfully, to visit the White House. But Mr. Kasich seemed determined to link himself to another Republican president, the conservative hero, Ronald Reagan, whose optimistic oratory he sought to evoke.

“The sun is rising, and the sun is going to rise to the zenith in America again,” Mr. Kasich said at one point, recounting his advice to citizens of an Ohio community whose economy was devastated by job losses during the recession. He wrapped up his speech with another Reagan-esque declaration: “The light of a city on a hill cannot be hidden. America is that city, and you are that light.”