The Friday statement says the decision to accept Ben Ali was made in light of "the exceptional circumstances the Tunisian people are going through" and with a "wish for peace and security to the people of Tunis."
No further details were immediately available.
In a statement, Obama says he applauds the courage and dignity of Tunisians who have been protesting soaring unemployment and corruption. The anti-government protests drove Tunisian President Zine El Abidine Ben Ali from power Friday after 23 years of rule.
Obama urged all parties to keep calm and avoid violence. He called on the Tunisian government to respect human rights and hold free and fair elections in the future.
The government says at least 23 people have been killed in the riots. Opposition members say the death toll is more than three times higher.