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Russia doesn't have the most positive reputation abroad. Many people, especially in the West, see it as an authoritarian state where riot police batter protesters and powerful forces repress homosexuals and other minorities. But now Russia is following the U.S.'s lead in a charm offensive.
Since Vladimir Putin first became a president in 2000, Russia has launched various projects to improve its image—a multilanguage TV channel, Russia Today, is one of the most visible endeavors—but they have not improved the nation's image as much as hoped, said Alexey Dolinskiy, a partner at consulting firm Capstone Connections.
"Numerous efforts to bolster its reputation abroad with foreign audiences have thus far not had the intended effect, especially in comparison to the amount of resources and attention invested by the Russian government," Dolinskiy said in a report, "Russia Direct. "
Dolinskiy told CNBC that, for example, Russia Today has managed to build a viewership but has not done much to materially change the country's image. Global attitudes toward Russia are more negative than positive, according to the 2013 GlobeScan poll. Among countries included in the survey, only a handful—Israel, North Korea, Pakistan and Iran—did worse.
Russia, now looking for more effective ways to bolster its reputation on the world stage, is borrowing tactics from Western governments.
After his re-election last year, Putin began pushing for Russia to build more "soft power." One way to do so is to provide unilateral aid to foreign countries, thereby presumably gaining international influence with them. In May, Putin signed a decree to broaden the authority of Rossotrudnichestvo, an agency in the Ministry of Foreign Affairs, to help in that effort.
Soft power is "the ability to get what you want through attraction and persuasion," said Joseph Nye, a political scientist at Harvard University, who coined the term more than 20 years ago. A country's culture, values and policies are sources of soft power, he said.
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The Russian daily newspaper Kommersant reported earlier this year that the country plans to reduce its funding to international aid organizations, which once ran at about $500 million annually, in favor of nationally branded projects—similar to the United States' assistance through USAID, the American Agency for International Development.
Government saw that help through international organizations does not give a necessary boost to Russia's image as the help comes to the countries under the brand of the international agency, like World Bank.
The budget for Rossotrudnichestvo could rise to 9.5 billion rubles (about $306 million), the daily reported, which it said would be an increase "of several times." Rossotrudnichestvo did not respond to CNBC's questions about future budget figures.
Putin's administration has made other moves. Public relations agency Ketchum reported that it received more than $1.9 million from the Russian Federation for services in the first half of the year.
Ketchum said it began its work with the Russian Federation during its presidency of the G-8 Summit in 2006, but it would not elaborate on the nature of its work, saying only that it's designed to create a "broader dialogue" between Russia and Western news media.
Russia Today gets about $400 million from the government each year, Dolinskiy said. But while the country's large-scale projects have created a platform to tell the world about its views, he said, they have not helped its image.
"In contemporary media you need to not just appear better but become better, " Dolinskiy said.
Russia faces different challenges with its image in different countries, said Valentina Feklyunina, a lecturer on politics at Newcastle University in the U.K. Her book on Russia, "Managing Russia's Image in the West," is scheduled to be released next year.
Feklyunina said that Western countries see Russia as a nondemocratic country, as a "country where authoritarianism is getting stronger lately." Putin's becoming the president for a third term had a negative effect, as did several other events, such as an adoption ban on the United States and pressure on homosexuals.
(Read more: Russia dealt triple blow over its economy)
"The image of Russia got worse after conflict with Syria," Feklyunina said. "Very often, Russia was perceived as a regime that supports Assad."
Russia has had limited experience in international development, Dolinskiy's report said, but giving aid under its own "brand"—especially within the former Soviet Union—"could result in greater ability by Russia to use international aid to project soft power around the world."
"Russia's soft power increased after the Cold War," said Nye at Harvard.
After the Soviet Union fell, other countries saw Russia becoming more democratic, he said, but in more recent years its soft power has been hurt by Putin's return to the presidency and cutbacks on personal freedoms, he said.
American democratic values may not be appealing to all countries, but they are relatively clear, Nye said. While traditional Russian culture is attractive to a foreign audience, people don't know much about its contemporary values.
"It is not clear what values post-Soviet Russia stands for," he said.
—By CNBC's Anna Andrianova. Follow her on Twitter