The pontiff's nephew, Emanuel Horacio Bergoglio, was critically injured in the crash on a highway in Cordoba, said Carina Ferreyra, a Cordoba police spokeswoman.
A car driven by Bergoglio struck a truck about 12:30 a.m., killing his sons -- Jose Bergoglio, 8 months, and Antonio Bergoglio, 2 -- and his wife, Valeria Carmona, 36.
Emanuel Bergoglio, 35, was taken to a hospital in Cordoba, where he was in critical condition Tuesday morning, Ferreyra said.
Pope Francis was "deeply hurt" by news of the crash, a Vatican spokesman said.
"The Pope has been informed of the tragic accident that took place in Argentina involving some of his family members," said the spokesman, the Rev. Federico Lombardi. "He asks to all of those who participate in his sorrow to be with him in prayers."
Pope Francis, the former Jorge Mario Bergoglio, served the Roman Catholic Church in Argentina for 43 years, including 15 years as archbishop of Buenos Aires. He succeeded Pope Benedict XVI as leader of the church in March 2013.
The 77-year-old pontiff recently visited South Korea, the first papal visit to the country in 25 years.
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