Only 9,500 of those fleeing for Russia have sought refugee status but many others are too afraid of future reprisals if they do return to Ukraine to make a formal request, said agency spokeswoman Melissa Fleming, citing official Russian figures and other UN information.
Another 750 Ukrainians have requested refugee status in Poland, Belarus, Czech Republic and Romania, according to UN figures.
The number of those internally displaced in Ukraine represents a huge increase since last week. Some 12,000 of them are from Crimea, which was annexed by Russia in March, and the rest are from eastern Ukraine, the Associated Press reported.
Inside Ukraine, the single largest concentration of refugees is in the town of Svyatogorsk in the Donetsk region, which has declared independence from the government in Kiev.
"The rise in numbers of the past week coincides with a recent deterioration of the situation in eastern Ukraine," said Fleming. "Displaced people cite worsening law and order, fear of abductions, human rights violations and the disruption of state services."
Many of the latest Ukrainians arriving are clustered in Russia's Rostov-on-Don region, where 12,900 refugees including 5,000 children have fled, and in Byransk, which has 6,500 refugees.
In Rostov, the refugees are being housed in public buildings and tented camps. Most of those in Byransk are staying with relatives or friends.