"Did we compete in 2008? No. So we won't compete in 2012."
Putin stepped down as president in 2008, after running for the maximum two executive terms in office.
Both Putin and Medvedev could run for the presidency in 2012, with a new six-year presidential term, which was approved by parliament earlier this year.
The prime minister, who is still widely seen as Russia's leader, reiterated his position that Medvedev was in charge.
"We have nothing to prove to anyone," he said.
"If someone lives in a dream, he needs to wake up, take a shower and look at reality. If you want to co-operate with Russia you need to know that it's the president who heads Russia."