LIMA, Peru—Ukraine Finance Minister Natalie Jaresko says she would resign if her coalition government backtracks overhauling the country’s conflict-ravaged economy, as rising support for populist parties threatens to erode support for the administration’s economic agenda.

Kiev’s failure to complete a 2016 budget—one that would meet the conditions agreed in a $17 billion International Monetary Fund bailout—is holding up the latest tranche of cash from the world’s emergency lender.

Ms....