WASHINGTON—Russian Finance Minister Alexei Kudrin, a darling of investors and one of the country's longest-serving officials, said Saturday he would decline a post in Russia's next government, just hours after Vladimir Putin announced he would stand for president in 2012 elections.

Mr. Kudrin cited differences with current President Dmitry Medvedev—who is expected to lead the next government as prime minister—on plans for ramped up military spending and other issues, saying Mr. Medvedev's policies carried "significant budget...