Describing Russia as a "regional power" and not the biggest national security threat to the US, Mr Obama said the country's forces would not be removed militarily from Crimea.
However, Obama said the annexation of the Black Sea region was not a "done deal" because the international community would not recognise it.
Following a nuclear security summit in The Hague, Mr Obama said: "It is up to Russia to act responsibly and show itself again to be willing to abide by international norms and … if it fails to do so, there will be some costs."
After scoffing at a decision by Mr Obama and his Western allies to boycott a G8 summit in Sochi in June and hold a G7 summit without Russia instead, the Kremlin said it was keen to maintain contact with its G8 partners.
"The Russian side continues to be ready to have such contacts at all levels, including the top level. We are interested in such contacts," President Vladimir Putin's spokesman said.
Mr Obama said he was concerned at the possibility of further Russian encroachment into Ukraine and believed Putin was still "making a series of calculations". He insisted Russian speakers face no threat in the country, contrary to Moscow's assertions.
He urged Mr Putin to let Ukrainians choose their own destiny free from intimidation, and said he was sure they would opt for good relations with both the European Union and Moscow rather than making a zero-sum choice for one against the other.
"Russia is a regional power that is threatening some of its immediate neighbours, not out of strength but out of weakness," Mr Obama said. "We [the US] have considerable influence on our neighbours. We generally don't need to invade them in order to have a strong co-operative relationship with them."
Asked what was to stop another Russian land-grab, Mr Obama drew a distinction between an attack on members of Nato covered by its Article V mutual defence clause, and on non-members where the West could apply international pressure, shine a spotlight on those states and provide economic support.
Ukrainian soldiers have started their withdrawal from Crimea, piling onto buses and leaving behind former comrades who saluted them from outside a base overrun by Russian forces.
Ukraine's acting defence minister, accused of crippling indecision, offered his resignation as the troops began their westward journey but was refused. Igor Tenyukh said he had received requests to leave Crimea from about 6500 soldiers and family members- meaning about two-thirds of the 18,800 military personnel and relatives stationed there are taking their chances in the peninsula newly absorbed by Russia.
In the western Ukrainian region of Rivne, Ukrainian ultra-nationalist leader Oleksandr Muzychko, better known as Sashko Bily, was shot dead in what officials describe as a special forces operation. He was killed by police as he tried to flee a cafe.
l The US House of Representatives Foreign Affairs Committee has passed a Ukraine aid bill that does not include International Monetary Fund reforms sought by the Obama administration and backed by Senate Democrats. It backs a $1 billion loan guarantee for Ukraine, includes sanctions on Ukrainians and Russians over Moscow's incursion into Ukraine and provides aid to Ukraine.