"I am very saddened by this, but what matters most now is the well-being of our kids," he told People magazine.
"I kindly ask the press to give them the space they deserve during this challenging time."
Jolie, 41, filed for divorce from Pitt, 52, citing irreconcilable differences on Monday.
Pitt and Jolie - nicknamed "Brangelina" by fans - married in 2014, 10 years after meeting on the set of 2005 film Mr & Mrs Smith.
It was Pitt's second marriage, having previously wed Friends star Jennifer Aniston, and Jolie's third after Thornton and Jonny Lee Miller.