Medvedev has so far received 69.22% of the vote with 70% of the ballots counted in Russia's presidential polls, according to Central Election Commission data. His nearest rival, Communist Party leader Gennady Zyuganov, is on 18.26%.
Speaking to journalists at a news conference, Medvedev said that his presidential program would be "the path chosen by our country eight years ago."
This path was, he clarified, the one "being followed by President Putin."
Russian First Deputy Premier Medvedev was publicly backed by Russian President Vladimir Putin as his successor in mid-December, and was later nominated by the ruling United Russia party as a presidential candidate.
Putin later announced that he would take up an offer by Medvedev to become prime minister if his 'heir' were to win the presidency.
Many political analysts suggested that Medvedev would struggle to make an impact as president with Putin as premier, and there were also suggestions that a change in the Constitution may give Putin more power.
However, Medvedev seemed to rule this out on Monday, saying that, "According to the structure of authority, the president has his own powers and the head of government his own. This is derived from the Constitution and the law. No one is proposing to change this."
The inauguration of Russia's new president is set for May 7.
Many Western observers, including the OSCE's main election arm, chose to boycott the election over restrictions imposed by Russia. Moscow rejected claims that it had imposed restrictions on monitors, however.
Critics also pointed to pressure on voters to cast their ballots, especially employees of state-run organizations. The refusal of the Russian election authorities to register a number of candidates from Russia's opposition due to 'irregularities' in their applications was also cited, as was the lack of media coverage of the candidates given permission to stand.
A CIS election monitoring mission said the elections had been held in full accordance with the law. The CIS is an alliance of a number of former Soviet republics.
Election monitors from the Parliamentary Assembly of the Council of Europe have yet to comment on the polls.
