Obama was speaking to US television before a busy day of diplomacy at D-Day commemorations in Normandy, France, where Russian President Vladimir Putin spoke briefly to Ukrainian president-elect Petro Poroshenko.
Obama, who also met informally with Putin, said he valued cooperation with Russia on issues including the Afghanistan war and the interim nuclear agreement with Iran. "But there is going to need to be a resolution of the situation in Ukraine," Obama told NBC Nightly News.
"And that requires Mr Putin to recognize that Ukraine just elected Mr Poroshenko the legitimate president, who will be sworn in on Saturday, (and) that Mr Putin should be working directly with Mr Poroshenko and the government of Ukraine to try to resolve differences between the two countries," Obama said.
Russia also needs "to stop financing and arming separatists who have been wreaking havoc in the eastern part of the country", Obama said, referring to the armed uprising in Ukraine that has claimed some 200 lives since mid-April. "If Russia begins to act in accordance with basic international principles, then I'm confident that the United States-Russia relationship will improve," he said.
Obama delivered a similar message in his meeting with Putin, said Ben Rhodes, a deputy US national security adviser.
Poroshenko – whose inauguration Saturday will be attended by US Vice President Joe Biden – said he was hopeful Russia would recognize his election after a "short delay".
The billionaire chocolate entrepreneur was strongly critical of Russia during his campaign. But Putin said after his meeting with Poroshenko that the incoming Ukrainian leader had the "right approach" to resolving the conflict.
Russia in March annexed Crimea, a strategic peninsula on the northern shore of the Black Sea, after a three-week occupation and a referendum which the UN General Assembly declared illegitimate.