The Virginia Republican said the GOP needs to work harder to connect with "an increasingly diverse country."
"Our party needs to do a better job at getting to know different constituencies," Cantor said while speaking at Harvard University's Kennedy School of Government. "I am much about trying to force that to happen."
Cantor's remarks were part of an ongoing effort to improve the GOP's image after painful election losses last November.
Cantor said that millions of Americans need help because they're suffering from a lack of education, skills, resources or time.
"One of my priorities this Congress will be to move heaven and earth to fix our education system for the most vulnerable," he said, endorsing plans for a new funding formula now being used in San Francisco public schools.
On immigration, Cantor stopped short of endorsing a comprehensive package, but said children of illegal immigrants should have a pathway to citizenship.
"I say if we're unable to get a comprehensive bill done first, at least we can start with the kids," he said.
The House Republican leader also called for prioritizing federal investment in medical research. Specifically, he called for shifting federal funding away from "less immediate" needs and toward finding cures for diseases.
The policy prescriptions are consistent with his message in recent public appearances.
Cantor only briefly mentioned Congress' recent inability to avert deep federal spending cuts—known in Washington-speak as "the sequester." They included sweeping reductions to some of the same policy priorities in Cantor's speech—education and scientific research, in particular.
Facing protesters who challenged him to support federal funding for a syringe exchange program, Cantor said the recent spending cuts require certain "tradeoffs."
"Unfortunately, that sequester takes a very blunt instrument and says across-the-board cuts to all of government," he said. "It eliminates or reduces, if you will, good programs the same way that it reduces bad. So I support research dollars. I support investment in the kinds of programs you're talking about. But yes, there are tradeoffs."