"What we have said to the Chinese -- and we've been firm consistently about this -- is you have to recognize that with increasing power comes increasing responsibilities," Obama told CNN's Fareed Zakaria, referring to ongoing disputes with China about aggression in the South China Sea, cyberattacks and economic policies.
Obama previewed the message he will send to Chinese President Xi Jinping at his last meeting with G20 world leaders.
"Part of what I've tried to communicate to President Xi is that the United States arrives at its power, in part, by restraining itself," Obama said. "You know, when we bind ourselves to a bunch of international norms and rules it's not because we have to, it's because we recognize that over the long term, building a strong international order is in our interests."
Obama said the US has been "very firm" in response to Chinese assertiveness, including in the disputed South China Sea, where the US has opposed territorial moves by China in contested areas.
"We've indicated to them that there will be consequences," he said.
Critics, however, have accused the US of not doing enough to check the rising power.
Obama is also expected to meet Turkish President Recep Tayyip Erdogan on the sidelines of the summit.
It will be their first meeting after a failed coup attempt in Turkey, which led to a crackdown on the nation's journalists and mass jailings.
Obama did not indicate the US would publicly rebuke Erdogan. Turkey remains an important ally in the fight against ISIS in the Syrian civil war on its borders, one of many shared interests.
"You now have a reaction (to the coup attempt) by the Turkish government that understandably is scared and concerned," Obama said. "Imagine if something like that happened here in the United States, the challenges that we would have in figuring out how to re-stabilize our country. ... We support the Turkish people, but like any good friend, we want to give them honest feedback if we think that the steps they're taking are going to be contrary to their long-term interests and our partnership."