Lauren Perkins of Pearland used her website to offer an update on the three boys and three girls.
The infants were born Monday at Texas Children's Hospital in Houston. Authorities say five of the babies, born about two months premature, are now breathing on their own.
Hospital officials say no updates on the infants will be provided until Monday.
Perkins was allowed to hold one of her daughters Thursday. She also says the baby who's sick has been making progress. The new mom did not elaborate.
The Houston Chronicle reports the children have been named Andrew Noah, Benjamin Luke, Levi Thomas, Allison Kate, Caroline Grace and Leah Michelle.