Ban arrived in Ukraine a day after holding talks in Moscow with Russian President Vladimir Putin during which he expressed his deep concern over the worst East-West crisis since the Cold War.
"This current crisis can only be resolved through peaceful diplomatic solutions based on the principle of the United Nations Charter, including respect for the sovereignty, unity and territorial integrity of Ukraine," Ban said after talks with Ukrainian acting president Oleksandr Turchynov.
"These are some of the most dramatic and serious times in the history of Ukraine," he said.
Ban added that the Crimean peninsula's absorption by Russia was becoming "a regional and even a global issue" that was diverting world leaders' attention away from other raging crisis such as the war in the Syria.
Turchynov for his part said Ukraine would never recognise the loss of its Black Sea peninsula to Russia.
"Ukraine will never accept the occupation of its territory... And will do its best to return Crimea," the acting president said.