"And therefore mentorship, or democraticising, or all the more so direct involvement from the outside is asolutely unacceptable, in our opinion," he said in remarks seen as thinly veiled criticism of the previous US administration.
"And understanding of this is growing in the world," Medvedev said, adding that Obama's speech in Cairo earlier this month provided evidence to that.
Medvedev's trip comes in the wake of that landmark address during which Obama sought to reach out to the Muslim world.
Obama is expected in Moscow on July 6-8 in an effort to revive frosty US-Russia relations, which took a beating under Obama's predecessor, George W. Bush.
Critics accused the Bush administration of trying to force democracy on countries like Iraq.
The Kremlin leader said attempts "to create a universal model of development, (and) spread that model through the entire world do not work and end up being a utopia and sometimes even a catastrophe."
Medvedev also said a new global order reflecting the world in its diversity was emerging "for the first time in centuries."
Russia is keen to boost its diplomatic clout in the region, which was a stronghold of Soviet influence before the end of the Cold War and the subsequent surge of US dominance.
As part of the Middle East diplomatic Quartet along with the European Union, the United Nations and the United States, Russia has been trying to organise a peace conference in Moscow since 2005.
Medvedev reiterated Russia's intention to host the conference by year's end, thanking his Egyptian host Hosni Mubarak for his support in that and saying he had secured principle support from all the parties involved.
Arab League chief Amr Mussa said his organization would support any steps that could help resolve the Palestinian-Israeli conflict.
Medvedev told the Arab League Russia supported a Palestinian state with the capital in east Jerusalem, saying efforts to finally solve the conflict should restart as soon as possible.
"There should not be a rollback here," he said, adding that the "prolonged pause" in the peace process was worrisome and the conflict threatened not only regional but also global security.
Medvedev also said Russia was an "inalienable part" of the Muslim world and was keen to cooperate with the Arab countries in the future.
Earlier Tuesday, he signed a 10-year strategic cooperation pact with Mubarak, with both nations saying there were committed to the "building of a new multipolar world order, which will be more democratic, fair and safe for all countries."
In a joint declaration, they said they were determined to coordinate "foreign policy positions and steps" and stressed the importance of reaching "a fair peace" in the Middle East.
With trade of 4.1 billion dollars last year, Egypt is Russia's largest commercial partner in Africa.
Russia has also expressed interest in a 1.5 billion-1.8 billion-dollar tender to construct Egypt's first atomic power station, which would resume the country's nuclear programme after a 20-year freeze.
A trade issue recently soured the economic ties when Egypt said recently it found impurities in a shipment of Russian wheat.
The Russian officials travelling with Medvedev Tuesday said the problem no longer existed, saying the countries agreed to boost quality control of the Russian grain shipments to Egypt.
Medvedev was due to visit key sites, including the Giza Pyramids, before leaving on Wednesday for Nigeria, Namibia and Angola for talks to expand the country's economic footprint in Africa.
------------------------------------------------------------------------------------------------------------------