A US official said the private session would be closed to the press.
The Obama administration has taken pains to ensure celebrations around the Suu Kyi visit does not detract from the simultaneous trip to the US of Myanmar leader Thein Sein, who has embarked on reforms.
Freed in 2010 after 15 years of being held under house arrest by Myanmar’s military regime, Suu Kyi has received a rapturous welcome on her first visit to Washington since her release.
She was also to receive the US Congress’ highest honor, the Congressional Gold Medal awarded in 2008 during her confinement.
Thein Sein is to address the United Nations General Assembly in New York, next week, as Myanmar slowly sheds its international pariah status.
On Tuesday, Suu Kyi thanked the United States for its support but said reforms must proceed without the pressure of sanctions and insisted improved relations with Washington would not pose a threat to Myanmar’s Chinese ties.
“In the end, we have to build our own democracy,” she said in a speech in which she appeared careful not to annoy leaders back home who have initiated reforms.