Putin is prohibited by law for running for a third consecutive term, but clearly wants to retain a powerful role once he steps down. Medvedev's proposal would provide such a role, especially if the constitution were amended to increase the prime minister's powers - which could be done readily with the new parliament dominated by pro-Putin politicians.
Medvedev, 42, has spent most of his career as a loyal comrade of Putin, and his proposal for him to become prime minister almost certainly was made with prior consultation with the president.
"Having expressed my readiness to run for president of Russia, I appeal to (Putin) with a request to give his principal agreement to head the Russian government after the election of the new president of our country," Medvedev said in televised address a day after Putin endorsed his candidacy.
"I think it is crucial for our country to keep Vladimir Vladimirovich Putin in the most important role in the executive branch - that of prime minister," Medvedev said.
virtually ensures that he will win the election.
"Medved" in Russian means "a bear," and his name coincides with the symbol of the pro-Putin party, United Russia - which has a brown bear on its party banner, says CBS News Moscow bureau chief Svetlana Berdnikova.
Medvedev also said that after the election, Russia must continue to pursue the policies driven by Putin in the past eight years.
Medvedev's support for Putin's policies and his proposal that he become prime minister were sure to raise questions of whether he would be a genuinely independent president or essentially a figurehead, doing Putin's bidding.
Medvedev, who projects a milder and more sympathetic image than the steely and often sardonic Putin, nonetheless echoed the prickly national pride and distrust of the West that characterize Putin's public statements.
"The world's attitudes toward Russia has been changed. They don't lecture us like schoolchildren. They respect us and they reckon with us. Russia has been returned to its overwhelming position in the world community," Medvedev said in a three-minute statement broadcast on state television.
He also praised efforts under Putin to restore the country's armed forces after years of post-Soviet neglect and underfunding, saying "Our military defense and security have been increased."
Despite the assertion of surging military might, Medvedev is not considered a Kremlin hard-liner, in contrast with the others who had vied for Putin's endorsement, chiefly fellow First Deputy Prime Minister Sergei Ivanov.
Both Medvedev and Putin worked under St. Petersburg's reformist Mayor Anatoly Sobchak in the early 1990s. After Putin became prime minister in 1999, he brought Medvedev to Moscow to become deputy chief of staff of the Cabinet. He then moved up to become deputy chief of staff for the president, was appointed to head the board of state natural gas giant Gazprom in 2002 and became full presidential chief of staff in 2003.
In 2005, Putin named him a first deputy prime minister.