"Black Widow has such a great back story, I would love to be able to explore that more, and we've talked about it," Johansson said at a news conference in Moscow.
"The Avengers", directed by Joss Whedon, is based on the Marvel Studio comics of the same name featuring superheroes teaming up to save the world from a looming disaster.
Both Whedon and "The Avengers" producer, Kevin Feige, have hinted at a sequel to the movie. Johansson said her family was originally from Minsk, Belarus.
"My mother is anxious for us to go there. I had a Russian language teacher and I learned it phonetically but I've forgotten everything now," she said.
Johansson's co-star Tom Hiddleston, who starred in the movie as supervillain Loki, said he liked Moscow and praised Russia's theatre culture.
"Five yeas ago, I came to Moscow to the Pushkin Theatre I think, I did some Shakespeare here. The theatre culture in Russia is amazing, you have the most diverse actors in the world, and there are theatres on every corner," he said. Hiddleston said he had spent "a very good time" in Russia and had "a huge affection for Moscow".