A proposed amendment to the agreement would effectively ban Americans from adopting Russian children to prevent abuse, RIA Novosti reported.
"So while I understand the position of those in favor of prohibiting the adoption of Russian kids by American families, I still believe that we have to try to keep the agreement," Lavrov told RT in an interview.
The adoption ban has passed the State Duma and will be reviewed by the upper chamber Federation Council on Wednesday.
If approved, it will then go to Russian President Vladimir Putin, who has not indicated whether he would sign it.
Lavrov had earlier criticized the proposed ban as "wrong."