Putin responded on Friday, saying: "We are firmly standing on both our legs and always look to the future, this is Russia's speciality and it is what has always allowed us to move forward and strengthen."
The Russian prime minister said that US-Russian relations could make a "great step forward" during the visit if Washington gave up its plans to place interceptor missiles and radar station facilities in Poland and the Czech Republic, or agreed to stop pursuing Nato expansion.
"If we see that our American partners stop the deployment of new military complexes, missile defence systems or, for example, reconsider their approach to expanding military-political blocs ... this would be a great step forward," he said.
Moscow reacted angrily to the US missile plan despite assurances from Washington that it are not directed against Russia.
The missile shield was strongly backed by Bush, but is now under review by the Obama administration.
Russia has also been unhappy about US support for expanding the Nato military alliance to include ex-Soviet republics such as Ukraine and Georgia.
Putin invited Washington to make a "huge step" towards improving US-Russian ties by repealling the Jackson-Vanik amendment, a Cold War-era measure that imposes trade restrictions on Russia.
Obama is scheduled to have a breakfast meeting with Putin on Tuesday, but the bulk of his talks will be with Dmitry Medvedev, the Russian president, who succeeded Putin in the Kremlin last year but who is often seen as less influential than his predecessor.
The US president said on Thursday that he had "a very good relationship" with Medvedev.
Despite the strong words, Putin said that Moscow was awaiting Obama's visit "with very warm feelings".
"And we say to the president of the United States, welcome," he said.