Sanjeev Chada was formally charged with the double homicide, the Irish Independent reported. He was being held on a suicide watch after a brief appearance before a judge late Thursday in Swinford.
Gary Walsh, a police detective in Castlebar, testified about Chada's reaction when he was charged with murder.
Walsh said Chada reacted after the second charge was read: "I'm so sorry, I really wish I hadn't done it."
Police found the bodies of Eoghan, 10, and Ruairi, 5, after Chada crashed his Ford Focus on Monday near Westport in County Mayo.
James Hanley, a solicitor who represented Chada during the hearing, said the 43-year-old, who lives in Ballinkillen, County Carlow, is unemployed and has no income. Hanley requested legal aid for his client.
The boys were to be buried Friday in a cemetery next to the school they attended.
Their mother reported them missing late Sunday after their father failed to bring them back after supposedly taking them bowling. He instead drove 150 miles from Ballinkillen in the southeast of Ireland to Mayo on the northwest coast.
Police believe the boys were killed on a rural road outside the village of Ballintubber and about half a mile from the historic 13th-century Ballintubber Abbey in County Mayo.
Couple mistakenly served bag of cash at McDonald's drive-thru
Kate Middleton recycles dress at movie premiere