In the letter, Lavrov asks how the countries react to the previous agreement that no country should strengthen its security at the expense of another country.
Russia believes that NATO is doing this by accepting Eastern European countries as new members.
The West does not share the view, but emphasizes that NATO's enlargement to the east does not threaten Russia's security.
In the answers, which according to Ekot will soon be handed over to Russia, NATO and the EU call for continued dialogue.
The bottom line in the answers is that the EU and NATO are prepared to talk to Russia, but not to shake up the current security arrangements, the radio reports.
The answers follow several days of discussions and aim, among other things, to show that the West is united with Russia.