MOSCOW — 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.

That alliance, however, appeared to be in jeopardy as Mr. Poroshenko and Mr. Kolomoisky clashed in recent days over the future of the two companies, UkrTransNafta and Ukrnafta, and as the president announced that he would take steps to incorporate militias like those controlled by Mr. Kolomoisky into Ukraine’s regular military.

The enmity comes as Mr. Poroshenko remains under tremendous pressure to demonstrate stability in spite of the continuing war and a collapsing economy that is being bailed out with tens of billions of dollars in international financing.