A year to the day after kicking off his victorious re-election campaign there, President Barack Obama returned to Ohio State University and told graduates that only through vigorous participation in their democracy can they right a poorly functioning government and break through relentless cynicism about the nation's future.

"I dare you, Class of 2013, to do better. I dare you to do better," Obama said.

In a sunbaked stadium filled with more than 57,000 students, friends and relatives, Obama lamented an American political system that gets consumed by "small things" and works for the benefit of society's elite. He called graduates to duty to "accomplish great things", like rebuilding a still-feeble economy and fighting poverty and climate change.

"Only you can ultimately break that cycle. Only you can make sure the democracy you inherit is as good as we know it can be," Obama told more than 10,000 cap-and-gown-clad graduates gathered for the rite of passage. "But it requires your dedicated, informed and engaged citizenship."

The visit to Ohio State for the first of three commencement addresses Obama will give this season was a homecoming of sorts for Obama, who has visited the campus five times in little more than a year, starting with his first official campaign rally here last May. He made many more stops elsewhere in Ohio as he and the Republican Mitt Romney dueled for the Midwestern state, which was pivotal to Obama's victories in 2008 and 2012.

There was little direct mention of party politics on Sunday, but ample allusion to the partisan battles that hindered many of Obama's legislative efforts in his first term and have continued unabated into his second. In an apparent reference to his failed push on gun-control legislation, he bemoaned that a small minority in Congress find excuses to oppose things that most Americans support.

"This is a joyous occasion, so let me put this charitably: I think it's fair to say our democracy isn't working as well as we know it can," Obama said.

Invoking the end of the Cold War, the 9/11 terrorist attacks and the economic recession, Obama said this generation had been tested beyond what their parents could have imagined. But he said young Americans have responded with a deep commitment to service and a conviction that they can improve their surroundings. He urged graduates to run for office, start a business or join a cause, contending that the health of their democracy "requires your dedicated, informed and engaged citizenship".

"You'll hear voices that incessantly warn of government as nothing more than some separate, sinister entity that's the root of all our problems," Obama said. "You should reject these voices. Because what these suggest is that our brave, creative, unique experiment in self-rule is just a sham with which we can't be trusted."

Ohio State also bestowed an honorary doctorate on Obama, applauding his "unwavering belief in the ability to unite people around a politics of purpose".

Also honored was photographer Annie Liebovitz, whose images of Obama and his family have become iconic reflections on the nation's first black president.

Obama's other two commencement speeches this season will be later in May at the US Naval Academy in Annapolis, Maryland, and at Morehouse College, an historically black, all-male school in Atlanta.