"Expressing my readiness to stand as a candidate in the presidential election, I ask (Putin) to agree to head the government of Russia after the election of the new president," Medvedev said Tuesday in a televised address.
On Monday, Putin endorsed Medvedev to succeed him as Russia's president, giving the soft-spoken deputy prime minister an overwhelming advantage in the country's March 2 elections. It is also a chance for Putin to retain some power with a long-time loyalist at the helm.
Putin has not yet responded to the offer, and many analysts say he may hold off on making an immediate decision on the prime minister post.
Russia's constitution bars Putin from holding a third consecutive term as president and requires that he step down in the spring. If Medvedev becomes president, then steps down from the post, dies in office or cannot execute his role, however, the constitution names the prime minister to serve as acting president until a new election can be held.
In the Russian government structure, the president's position as chief of state holds more power than the prime minister with control over the security forces, armed forces and the judiciary. The prime minister - who is appointed by and can be dismissed by the president - holds a lower role as the head of government.
But while Putin's United Russia party holds control of parliament, he could shift more powers to the prime minister's office, either by passing laws or amending the constitution, before he steps down as president.
Medvedev is known as a Putin loyalist and has served as first deputy prime minister since November 2005. He is also the chairman of Gazprom, the world's largest gas company, which accounts for 20 percent of the world's global supply. After Monday's announcement, many in the oil and investment industries welcomed the nomination, saying it was a good move for business and Russia's relations with the West. Gazprom's stock rose 2.5 percent, according to Reuters.
"The arrival of Medvedev will result in the implementation of the agreed gas-liberalization plan," said Steven Dashevsky, head of research at UniCredit in Moscow, to Reuters, referring to a plan to raise domestic gas prices to match gas export prices. "But I would take a step further," Dashevksy continued, "and say that the implications are for a more reform-oriented economy as a whole."
As president, Medvedev said he would continue the reforms and policies implemented under Putin in the last eight years, including improving living standards across Russia and asserting it as a player on the world stage.
"Russia is different now, much stronger and better-off," Medvedev said, according to news reports. "We are being respected and we are being listened to. We are not being treated as schoolchildren."