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Miles (34) who is pregnant, was in stable condition and her unborn child was doing well, agent Dustin Flores said by email.
The accident occurred on Monday in the New York City borough of Brooklyn when a driver lost control and hit five people, New York City police said.
Miles' daughter Abigail and the 1-year-old son of Miles' friend, Lauren Lew, were pronounced dead at a hospital, police said.
Miles won a Tony award for best featured actress in a musical in 2015 for her role as Lady Thiang in the revival of Rodgers and Hammerstein's The King and I.
The mezzo-soprano has a recurring part on the FX cable series, The Americans.
Flores said that Miles was scheduled to perform in The King and I in London's West End this summer and it was unclear if that would change.
A GoFundMe page set up to raise an emergency fund for Miles had received more than $US250,000 from nearly 5000 people in 15 hours. A separate fund for Lew had raised more than $US100,000.