Mr. Lyashko has denied any connection to crimes or oligarchs and said that his opponents are constantly trying to smear him with all sorts of allegations.

He certainly has enemies. On Wednesday, he canceled all of his remaining campaign events for the week after the state security service warned him of a planned assassination attempt.

In the interview, he said his critics in the establishment have it backward: They are the problem. “I think I’m smarter than they are,” he said. “They pretend to know everything, to know how to do everything, but we see the results of their politics.”

“My performance might look plainer, maybe primitive to some point,” he said. “Better I be a populist than to be the authorities who are desperately different from people, and don’t understand people’s problems and how to solve them.”

It is not hard to grasp the appeal of his message.

As chief of the Radical Party, in a country that remains at war, and is suffering from more than two decades of government corruption and mismanagement, Mr. Lyashko calls for — no surprise here — “radical reforms,” including changes to end government corruption and force the wealthiest businessmen to pay their fair share of taxes, to rebuild the military, to increase salaries and pensions, to join the European Union and NATO, to end Russian influence, to stop borrowing so much from the International Monetary Fund and other foreign creditors. The wish list is long, with few explanations of how to afford or accomplish it.

“To save our country, we need to act quickly and forcefully,” he said.

PERHAPS most controversially, he calls for rebuilding Ukraine’s nuclear arsenal, once the world’s third largest after the breakup of the Soviet Union. Ukraine gave up its nuclear weapons as part of an agreement in 1994 with the United States and Russia that called for respecting Ukraine’s borders and territorial sovereignty — an accord breached by Russia’s annexation of Crimea.

Alyona Getmanchuk, the director of the World Policy Institute, a political research organization in Kiev, said Mr. Lyashko was filling a populist niche once dominated by former Prime Minister Yulia V. Tymoshenko, who has fallen out of favor with voters. Ms. Getmanchuk said that his appeal was strongest among rural, less educated voters, and that he was running against the political establishment, though he is actually a part of it.