Putin has also said he would accept the position of prime minister in any new administration, a move which his critics say would still leave him in real control of Russia's affairs.
Opponents and many international observers are already calling the election a sham, saying the state-controlled media has been pro-Medvedev, and his opponents have been given limited coverage.
Al Jazeera's Jonah Hull in Moscow says that so far there are very few election monitors in Russia further raising fears that the vote will not be entirely democratic.
Lavrov denied suggestions that the election would inevitably be viewed as flawed and said that the majority of Russians were happy with the democratic processes in their country.
"It's our country, it's our democracy, which is young but which is evolving," he told Jonah Hull on Thursday in an exclusive interview with Al Jazeera.
"As far as I can feel the mood of the Russian people they are behind the present course, and the course I am convinced 100 per cent would be continued and developed even more after the presidential elections.
"Any responsible criticism might be voiced abroad we would be ready to listen to. What we cannot accept is absolutely biased or unjustified accusations that we are moving in the wrong direction."
Western leaders are waiting for the outcome of the presidential election, and on Thursday Bush said it would be interesting to see who who shows up for Russia at the next summit of world leaders.
Bush was asked at a news conference about the future of one of the nation's most important foreign relationships, one that has been increasingly troubled.
He said he, too, was eager for insights into "how Russia intends to conduct foreign policy after Vladimir Putin's presidency. And I can't answer the question yet".
|Lavrov says Russia's foreign policy is |
not aimed at confronting the US
Bush is not the only senior politician in the US who is unfamiliar with Medvedev.
Hillary Clinton, a leading contender to succeed Bush, stumbled for Medvedev's name in Tuesday's presidential debate before coming up with, "Medvedev - whatever".
Nevertheless, she said Medvedev was someone "who Putin can control, who has very little independence, the best we know".
Relations between the US and Russia have become strained recently over a number of issues including missile defence.
Open and 'constructive'
Lavrov told Al Jazeera that Russia has always been open and "constructive" about its foreign policy intentions and that "many of these problems [with the US] seem to us artificial."
"There is not necessarily a misunderstanding [of Russia], but an inertia of the cold war logic which was to a large extent based on containing Russia," Lavrov said.
"None of Russia foreign policy is designed to combat US. Of course the US is the dominant player in world affairs, it's an objective fact.
"But at the same time recent history has shown, in Afghanistan, in the Middle East that no one power can resolve regional and international problems on its own, whatever powers it possesses."