"My hope is that the president-elect coming in takes a similarly constructive approach, finding areas where we can cooperate with Russia where our values and interests align, but [that] the president-elect is also willing to stand up to Russia where they are deviating from our values and international norms," he said.
Obama went on to say that he doesn't expect Trump to follow his administration's "blueprint exactly," but said he hopes Trump doesn't just focus on practical objectives, in the manner of realpolitik.
"My hope is that he does not simply take a realpolitik approach and suggest that if we just cut some deals with Russia, even if it hurts people or even if it violates international norms or even if it leaves smaller countries vulnerable or creates long-term problems in regions like Syria, that we just do whatever is convenient at the time," he said. "And that will be something that we’ll learn more about as the president-elect puts his team together."
Obama added that he is encouraged that Trump told him "NATO is a commitment that does not change."
He also warned against taking for granted the democratic process and form of government.
"We have lived in an era that has been largely stable and peaceful ... where living standards have generally gone up. ... [There's a] tendency to assume that’s always the case. And it's not. Democracy is hard work," he said. "In the United States if 43 percent of eligible voters do not vote, then democracy is weakened."
He continued: "If we are not serious about facts and what’s true and what’s not and particularly in the age of social media where so many people are getting their information in soundbites and snippets off their phones, if we can’t discriminate between serious arguments and propaganda, then we have problems. ... [If we are] unable to compromise and engage in the democratic process and taking absolutism views ... then democracy will break down."
Obama cautioned against comparisons between "overzealous politicians" in the U.S. and governments of oppression.
He also said he told Trump during their meeting last week that the work of the presidency is very different from "generating enthusiasm or passion" on the campaign trail.
"He’s indicated his willingness, his understanding of that, but you’re absolutely right that that has to reflect itself not only in the things he says, but also in how he fills out his administration, and my hope is that that’s something that he’s thinking about," Obama said of Trump.
"Because not only is the president of the United States somebody that the entire country looks to for direction, but sets the agenda internationally in a lot of ways," he added.
Obama said he's "cautiously optimistic" about Trump because the demands of the job of president of the United States "force you to focus."
He then qualified with this warning: "If you’re not serious about the job, then you probably won’t be there very long."