Day four of the Libyan intervention, and it’s not just in the West that it’s provoking ideological confusion and fracturing old alliances.

Today’s instance is from Russia, with a sharp difference of opinion between president Dmitry Medvedev and his prime minister, Vladimir Putin.

Speaking at, of all places, a Russian missile factory, Putin expressed serious concerns about the Libyan campaign and the security council resolution that authorised it, likening it to “medieval calls for crusades”. “I am concerned by the ease with which decisions to use force are taken in international affairs. This is becoming a persistent tendency in US policy.”

So far, quite consistent with Putin’s often-expressed views. What was unusual was the rapid rebuke he received from Medvedev, who described his remarks as “unacceptable”. According to the president, the UN resolution was not out of line with Russian policy: “That’s why we did not use our veto right … those were my instructions to the foreign ministry and they have been implemented.”

Russia’s political system is designed broadly on the French model, a hybrid of Westminster and American traditions: the head of government is a prime minister responsible to the legislature, but the president, who appoints the prime minister, is more than just a figurehead and has significant independent power, especially in foreign affairs.

That’s the theory, at least. Many observers, however, regard Medvedev as a puppet and Putin as the real boss: he was president for two terms, retiring in 2008 due to term limits but promptly being appointed prime minister by Medvedev, his chosen successor. It has been widely suggested that at next year’s presidential election they would swap places again.

Medvedev’s rhetoric is consistently more liberal and democratic than Putin’s, making him more of a favourite with Western leaders. Their views on Libya fit the pattern: Medvedev wants to align Russia more closely to the West, while Putin, by habit an authoritarian leader, has an instinctively negative reaction to the idea of foreign intervention to protect people against their government.

But it’s harder to point to actual differences in policy between them.

There’s a fairly widespread view that what they have is just a well-honed “good cop, bad cop” routine, in which Medvedev presents the friendly face of authoritarianism to the world while Putin actually runs the show.

No doubt there’s an element of truth in this, but if today’s public disagreement between the two men was just an act, it was a very elaborate one. It’s more plausible to think that Medvedev means what he says and that, having been in the job now for almost three years, he is becoming more jealous of his prerogatives and perhaps a little resentful of Putin’s presumption.

If that’s the case, then the lead-up to next year’s election is going to be very interesting. At the very least Medvedev will take some persuading before giving up the top job, and if he wins a fresh mandate he may be even more keen to stamp it with his own personality. Although he and Putin have previously promised not to run against each other, a genuine contest between them could be a very good thing for Russia’s fragile democracy.

Putin, however, remains the experienced politician — Medvedev had never held elective office until he won the presidency. And Putin has the runs on the board; under him, Russia has enjoyed the sort of stability and prosperity that his predecessors only dreamt of. There’s no likelihood that Medvedev will feel able or willing to dispense with his services.

But today he’s shown a willingness to clip his prime minister’s wings a little.