There has been speculation for months in the media and among political analysts that Putin, now 60, could make Medvedev a scapegoat if Russia's economy continues to decline.
Medvedev hit back after unauthorised video footage showed Putin threatening to sack unnamed senior officials over a failure to implement his social spending plans - for which responsibility ultimately lies with Medvedev's government.
Putin had just told the cameras to stop rolling at a meeting with regional officials and government ministers, and his angry, unguarded remarks revived months of speculation that he has lost confidence in Medvedev.
Medvedev, 47, who has been prime minister since last May, asked for parliament's support in a long-planned report on his government's work that lasted an hour and 45 minutes.
"We live in a dynamic, fast-developing world. It is so global and so complex that we sometimes cannot keep up with the changes," he said, acknowledging that Russia could be dragged into recession if global commodity prices keep falling.
"On the other hand, we live in a society that offers huge opportunities. So I hope that ... Russia tomorrow will be a country that is strong and comfortable to live in."
In a rallying cry to parliament, he called for unity and respect for his government's work.
But, deepening his problems, Communist Party chief Gennady Zyuganov criticised Medvedev's performance and said he should "draw the conclusions". The Just Russia party threatened to call a no-confidence vote if Russia sinks into recession.
Medvedev would have every chance of surviving such a vote, because the State Duma, the lower house, is dominated by his and Putin's United Russia's party. But retaining Putin's support is vital for his political future.
Medvedev said he had plans for improving the economy, which is heavily reliant on exports of oil and gas, but gave few details, reiterating his refusal to raise the pension age and saying he would not sell off state assets cheaply.
He said Russia risked sliding into recession because of falling commodity prices, and that the government would consider other stimulus measures to push growth closer to the target rate of 5 percent this year if an economic slowdown continued.
Last year the economy grew 3.4 percent, and last week the government cut its growth target for 2013 to 2.4 percent.
Putin and Medvedev have been allies since working together in the St Petersburg city administration in the 1990s, and swapped jobs last May after Putin won a third term as president after four years as prime minister.
In the footage, published online shortly before Medvedev started his speech to parliament, and later shown by state television, a stern-looking Putin called for more action to fulfil pledges he has made on social spending to improve the lives of millions of Russians.
Putin had made the promises as he tried to win back support after the biggest protests of his long rule.
"If we don't do it, we will need to acknowledge that either I work inefficiently or you work badly and you will need to resign," he told Tuesday's meeting in the footage published by the Lifenews.ru website, which has close ties with the Kremlin.
"I would like to draw your attention to the fact that I am currently inclined towards the second scenario."
Putin's press secretary denied the president was referring to sacking the government but the remarks were widely seen as a warning. The Kremlin's anger over the footage - Lifenews said it had been barred from the presidential pool - also underlined the sensitivity of Putin's comments.
A professionally produced video by an anonymous filmmaker, posted on YouTube earlier this year, used archive footage and apparently recent interviews to present Medvedev as weak and ready to surrender Russian interests to a conniving United States. The word "treason" is uttered by a narrator.
Moscow Mayor Sergei Sobyanin is among the list of potential replacements for Medvedev, but Putin has a record of loyalty to his long-standing allies and many political observers say he would remove Medvedev only reluctantly. A significant change of policy would be unlikely as this is dictated by Putin.