Prince William said it had been an “anxious” start but added that the Duchess is doing “well”.
“We need Catherine to get over this first bit and then we can start celebrating,” he said, during a visit to the National Mental Health and Policing Conference on Tuesday 5 September.
The Duke added: “It’s always a bit anxious to start with, but she’s well.
“There’s not much sleep going on at the moment.”
The Duchess is suffering with hyperemesis gravidarum (HG), a severe pregnancy sickness that she also experienced during her two previous pregnancies.
Due to her condition, the Duchess will no longer carry out planned royal engagements.
HG is prolonged and severe nausea and vomiting, which is estimated to affect around one in every 100 pregnant women.
It’s not known what causes HG, but according to the NHS, some experts believe it is linked to changing hormones during pregnancy.