Dozens of international firms doing business in Russia have pledged not to offer bribes, in a move aimed at fighting corruption collectively.
The accord, signed at an official ceremony in Moscow, was initiated by the companies, not the Kremlin, said the Russian-German Chamber of Commerce.
Anti-corruption group Transparency International has said bribery in Russia is worth $300bn (£195bn) a year.
Two recent bribery scandals in Russia have involved foreign firms.
The agreement was praised by Russian presidential adviser Arkady Dvorkovich.
"We are glad that foreign companies have heard us and are ready to help us fight corruption," he told Russian business daily Vedomosti.
Among more than 50 predominantly German companies which signed the agreement were Siemens, Deutsche Bank, Deutsche Bahn and Axel Springer AG.
Russian President Dmitry Medvedev has declared fighting corruption to be one of the main goals of his presidency.
Last week he signed a decree outlining his government's approach to tackling the problem.
Recently there have been two high-profile bribery scandals in Russia involving international companies.
Russian, German and US authorities are investigating whether US computer company Hewlett-Packard paid millions of dollars in bribes to win a big contract in Russia several years ago.
A spokesperson for Hewlett-Packard said last week that HP would "continue to fully co-operate with the authorities investigating this matter".
"This is an investigation of alleged conduct that occurred almost seven years ago, largely by employees no longer with HP," the spokesperson said.
Also, German carmaker Daimler agreed to pay $185m to settle a US corruption case involving offences committed in Russia.
However, the executive director of the Russian-German Chamber of Commerce, Michael Harms, called it "a coincidence" that international companies signed the anti-bribery agreement only days after Mr Mededev unveiled the recent official policy and the two bribery scandals became public.
"We have been working on it [the agreement] for half a year, we would not be able to do it just in a week," .
Mr Harms said that German companies doing business in Russia were the first to lay down the collective measures against corruption.
He admitted that the task of tackling corruption in Russia was a difficult one, but said that it could be achieved "in the long run".
Elena Panfilova, head of Transparency International in Russia, said that the anti-bribery agreement was "good rather than bad".
She added, however, that any company working in Russia could find itself in a situation when it did not want to give bribes but was forced to do so if it wanted to carry on doing business. The agreement would not solve situations such as these, she said.
Robert Mitchell, head of enhanced due diligence for Europe, Middle East and Africa at risk specialist World-Check, said that governments were responsible for dealing with the problem of corrupt officials.
"They [governments] have to practice what they preach," he said.
Mr Mitchell added that the way to try to solve the problem in Russia was to follow in the footsteps of western countries and blacklist individuals and companies who were responsible for receiving bribes.
Traditions different from those in Russia, as well as tougher laws in their home markets, could be the reason why, according to Mr Harms, foreign companies have been much more eager to join the anti-bribery initiative than Russian firms.
Several corruption scandals involving international companies working in Russia became public not as a result of Russian officials' moves, but after prosecutors in Western countries took action.
"Western companies think that even if things remain hidden in Russia, they will be uncovered at home," said Ms Panfilova.
"In Russia, it is a different story."
Most experts agree that foreign companies' readiness not to offer bribes in Russia is a good sign, but it will not be enough to eradicate corruption any time soon.
Mr Harms believes that this time the companies signing the agreement have managed to come up with a mechanism to fight corruption on day-to-day basis.
But critics say it is not yet clear whether declarations of intention will be followed by effective actions.
History shows that in terms of successfully fighting corruption in Russia, not a lot has been achieved so far.