Talking in Berlin, Mr Obama said he trusted the US president-elect would "not just adopt a realpolitik strategy" to managing Russia.
He likewise cautioned against a digital weapons contest, saying there was clear evidence Russia had occupied with digital assaults.
Mr Obama was talking after converses with the German Chancellor Angela Merkel.
The two close partners focused on the requirement for proceeded with close co-operation between their nations, and also between the US and EU overall.
Mrs Merkel recognized that the US had "carried the majority of the weight" of the Nato collusion - a difference scrutinized by Donald Trump - and said European nations "should in future... connect with all the more, so that in the long haul the awkwardness in resistance spending is destroyed".
In pictures: Obama-Merkel relationship
Trump's severe shock for Germany
Trump and exchange: A radical plan?
Russian "interfering"
Mr Obama said he trusted Mr Trump would look for a helpful association with Russia, "discovering ranges... where our qualities and interests impact".
In any case, he included that he trusted Mr Trump was "ready to face Russia when they veer off from our qualities and universal standards".
This implied, he said, shunning taking a "realpolitik approach" and cutting arrangements that could "hurt individuals or... damage universal standards... leave littler nations defenseless, or make long haul issues in areas like Syria".
On the issue of digital assaults, Mr Obama said there was a distinction between "Russian knowledge assembling" and "interfering with races or following private associations or business elements".
He said he had "conveyed a reasonable and mighty message that.... we're checking it precisely and we will react properly if and when we see this event".
He additionally had this notice for youngsters: "Don't underestimate our frameworks of government and our lifestyle... Majority rules system is diligent work."
Trump chose - full report
Obama at the Brandenburg Entryway on 17 November 2016Image copyrightAFP
Picture inscription
Barack Obama landed in Berlin late on Wednesday
Why Germans will miss Obama: By Jenny Slope, BBC Berlin journalist
At the point when Barack Obama came to Berlin in 2008 he was welcomed like a demigod.
A huge number of cheering Germans turned out for the then presidential competitor and thundered their endorsement of his vision of another America - one which would be interested in, and co-work with, whatever remains of the world. His liberal and conciliatory tone inspired an emotional response with numerous in the energized swarm.
Couple of here are cheering at this point.
Click here to peruse whatever is left of Jenny's article
Mr Obama and Mrs Merkel have had a nearby working organization in the course of the most recent eight years and had warm words for each other. She told columnists "the separating is hard for me", while he called her an "exceptional accomplice".
Germans are expected to go to the surveys in the pre-winter of one year from now after three sequential terms in office for Mrs Merkel.
While she has not yet chose whether to stand once more, Mr Obama told voters he had valued her "uprightness, her honesty, her astuteness."
Amid Thursday's discussions, the two pioneers additionally talked about the emergencies in Ukraine and Syria and the battle against purported Islamic State.
Mr Obama is relied upon to hold chats with UK Head administrator Theresa May and the pioneers of France, Italy and Spain on Friday, before traveling to Peru.
'Love is flying out of a window': German media response
German media have embraced an elegiac tone in their scope of Mr Obama's visit, noticing that the cozy relationship between the active US president and the German chancellor is probably not going to be rehashed with Mr Obama's successor.
Center Online says these are "bleak days" for Mrs Merkel, as this may be "the last time that she will have Barack Obama next to her as president of the Assembled States. It is far fetched that the chancellor will have the capacity to fashion an also cozy association with Obama's successor Donald Trump".
A few outlets depict the visit as the last blooming of a political relationship that was at first ease back to go ahead.
Regular of these is Zeit On the web, which conveys the feature "Merkel and Obama: Late Love" and says: "This is the tale of a rapprochement between two contradicting lawmakers. What's more, of how they were at last ready to get together. The critical variable was their common liberal perspective of the world."
What's more, in the newspaper Bild, editorialist Franz Josef Wagner delivers an open letter to Mr Obama in which he composes: "Saying farewell is troublesome for me. It's as though love is flying out of a window, similar to a butterfly. After Obama we have Trump, and I am shutting the window."
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