"It's a long race. We're going to go through South Carolina, ultimately to the Midwest," Kasich told ABC News' George Stephanopoulos on "Good Morning America" this morning. "This is a long, long race."
"Everybody always underestimates me," he added.
Kasich's home state of Ohio is a crucial winner-takes-all delegate prize. Ohio residents do not cast their votes until mid-March.
Kasich also insisted that he can unite the Republican party - including backers of Donald Trump, who won the New Hampshire contest by almost 20 percentage points.
"We can attract the Democrats," he said, talking about the general election. "We're Americans before we're Republicans and Democrats."
He went on to lament what he said are the negative states of his rivals' campaigns, particularly that of former Florida Gov. Jeb Bush.
"I think it's a sad situation," he said. "I'm not going to get diverted by it."
"The light really does overcome the darkness," he continued.