The U.S. has demanded that Russia send Snowden home to face prosecution for espionage, but President Vladimir Putin dismissed the request.
Putin had said that Snowden could receive asylum in Russia on condition he stops leaking U.S. secrets. Kucherena has said Snowden accepted the condition.
The Guardian newspaper on Wednesday published a new report on U.S. intelligence-gathering based on information from Snowden, but Kucherena said the material was provided before Snowden promised to stop leaking.
Snowden, who revealed details of a U.S. intelligence program to monitor Internet activity, has received offers of asylum from Venezuela, Nicaragua and Bolivia and said he would like to visit those countries. However, the logistics of reaching any of those countries are complicated because his U.S. passport has been revoked.
The Snowden case has further strained U.S.-Russian ties already tense amid differences over Syria, U.S. criticism of Russia's human rights record and other issues.
Snowden's father said in remarks broadcast Wednesday on Russian television that he would like to visit his son. Kucherena said he is arranging the trip.