The ministry said it received the letter from Eric Holder July 24, Xinhua reported.
However, it did not specify the nature of the reply and the exact date it would be ready.
Holder assured his Russian counterpart Alexander Konovalov that "the US would not seek the death penalty even if Snowden were charged with additional, death penalty-eligible crimes".
His letter came amid media reports that Snowden had applied for political asylum in Russia on the grounds that if he were returned to the US, he would be tortured and would face the death penalty.
The top US lawyer said these claims were "entirely without merit. Torture is unlawful in the US".
He said Snowden was able to travel though his passport had been revoked. "He is eligible for a limited validity passport good for direct return to the US".
The 30-year-old former CIA contractor arrived at Moscow's Sheremetyevo international airport June 23 and has reportedly been stranded in the transit zone. He faces espionage charges as he disclosed a classified intelligence surveillance project code-named PRISM.
Kremlin spokesman Dmitry Peskov earlier said Russia would not hand Snowden over to the US.
--IANS (Posted on 28-07-2013)