Cornelia Streeter was reunited with her children Wednesday night after a separation of nearly two years, attorney Barry Pollack said from Boston.
Streeter "is extremely appreciative of the prompt, sensitive and effective way that the Cuban authorities have handled this matter," Pollack said.
The Topsfield, Mass., woman and her children were at an undisclosed location in Havana on Thursday.
In a case that recalled the battle over young castaway Elian Gonzalez, state-run television reported late Wednesday that authorities took action after confirming that Streeter had sole custody of the children. U.S. court records identify them as Henry, 9, and Victoria, 7, but Cuban authorities listed them each as one year older.
The report said the children were born during Streeter's marriage to Anwar Wissa.
Both Massachusetts senators, Edward Kennedy and John Kerry, applauded the reunion. Kennedy said he is "grateful for the assistance we received from the U.S., Egyptian, and other governments."
Streeter made her appeal in a letter, which was delivered to the Cuban president by a "friend of our commander in chief," said the government statement read on the nightly news broadcast.
The children were found at a Havana marina, where Wissa was staying with them on a yacht, the statement said. Wissa, also an American citizen, was arrested.
The statement said Cubans remain mindful of the Elian Gonzalez case and the support most Americans showed for the child's return to his father.
"For that, we owe the American people our gratitude and respect," the statement said.
Elian was 5 years old in November 1999 when he was rescued at sea off Florida following a boating accident that killed his mother and other Cubans trying to immigrate illegally to the United States.
Elian's great-uncle fought unsuccessfully to keep the child in Miami during a dramatic custody battle.
The Cuban statement said an investigation showed that after Streeter and Wissa divorced two years ago, they initially had joint custody. But Streeter was later granted sole custody.
According to the statement, Wissa faces criminal charges in Massachusetts and U.S. federal courts for kidnapping the children.
By Anita Snow