Although Medvedev is seen as Putin's protege, he appeared to issue a veiled criticism of Putin's policies on Tuesday.
The president said that the cabinet's programme for tackling the country's economic problems was "well-balanced but not ideal".
The president quickly toned down his criticism by saying that "no ideal programs exist" but some saw it as a rare visible crack in the Putin-Medvedev ruling axis.
Dmitry Oreshkin, an independent political analyst, was quoted by Gazeta.ru, an online Russian newspaper, as saying that "Medvedev may wait until Putin loses his popularity as the economy worsens by the day and dismiss him".
However, most analysts still expect Medvedev would step aside if asked to by Putin.