Bush's carefully couched message on Wednesday was his first official comment on Putin's recent proposal to do away with elections for governors in Russia's 89 regions.
Candidates would instead be selected by the president and approved by regional assemblies.
Putin has justified the move as needed to crack down on terrorism after a school hostage crisis in Beslan in southern Russia left more than 330 people dead.
But Putin's critics say the Russian president is exploiting the siege to amass more power.
Bush said he had recently spoken to Putin to express his condolences about the Beslan deaths.
"I am also concerned about the decisions that are being made in Russia that could undermine democracy in Russia; that great countries, great democracies have a balance of power between central governments and local governments," he said.
The Beslan school siege prompted
Putin to take the new measures
Bush also stressed on the need for a balance of power "within central governments, between the executive branch and the legislative branch and the judicial branch".
A Bush aide said the president's message was "not a rebuke, but an expression of concern".
Bush himself has ironically been under fire at home for impinging on American civil liberties through the anti-terror Patriot Act legislation.