"The project is closed. This is it," Miller, who accompanies Russian President Vladimir Putin during his official visit to Turkey, told reporters in Ankara.
Earlier on Monday, the Russian president said that Russia was unable to continue the implementation of the South Stream pipeline project in light of the European Commission's "non-constructive" stance on the matter.
"We can see that the obstacles are being created in its implementation. So, if Europe does not want to implement it, it means that it will not be realized," Putin said.
Gazprom announced the construction of a pipeline across the Black Sea to reduce the possibility of unreliable Russian gas passage to central and southern Europe through Ukraine in 2012. South Stream was expected to be fully operational by 2018.