MEXICO CITY—The government of Guatemalan President Jimmy Morales on Monday said it was unilaterally withdrawing from a United Nations-backed anticorruption commission and ordering its prosecutors and investigators to leave the country within 24 hours, exacerbating a political crisis.

The move by Mr. Morales steps up a showdown that began in mid-2016, when the International Commission Against Impunity in Guatemala, known by the acronym CICIG, said it was investigating the president for alleged campaign finance violations during...