Ethiopia has banned the adoption of children by foreigners amid concerns they face abuse and neglect abroad.
Ethiopia is one of the biggest source countries for international adoptions by US citizens, accounting for about 20% of the total.
Celebrities Brad Pitt and Angelina Jolie are among those who have adopted children from Ethiopia.
However, in 2013, a US couple were convicted of killing an adopted Ethiopian girl.
That case triggered a debate about foreign adoption, the BBC's Emmanuel Igunza in Ethiopia's capital Addis Ababa says.
The adoption process in Ethiopia has also faced serious questions with rights groups saying that it was prone to abuse by human traffickers who saw it as lucrative market.
Two years ago, Denmark stopped the adoption of children from Ethiopia.
Lawmakers now say orphans and other vulnerable children should be cared for under locally available support mechanisms in order to protect them.
But some MPs said that the country has insufficient local services to cater for vulnerable children.
More than 15,000 Ethiopian children have been adopted in the US since 1999.
Many are also taken to European countries such as Spain, France and Italy.