A dispute between President Petro O. Poroshenko of Ukraine and the billionaire governor of one of the country's regions over control of two state-owned energy companies widened Monday, confronting the new Ukrainian government with its most serious internal crisis since coming to power last year.

Until the dispute burst into the open last week, the governor, Igor V. Kolomoisky, had been among the Kiev government's staunchest allies. Militias financed privately by him have played a crucial role in stopping pro-Russian separatists waging war in the east from advancing into the heart of Ukraine.