Russia has rejected criticism from the United States that reforms designed to overhaul national security could undermine democratic development.
Putin announced the new measures on Monday
Foreign Minister Sergei Lavrov said the new measures were a domestic matter which should not concern the US.
US Secretary of State Colin Powell said on Tuesday that Russia was in effect pulling back from democratic reforms.
The European Union's Chris Patten has backed Mr Powell's remarks, urging respect for human rights and democracy.
Mr Patten, the EU's external relations commissioner, made his remarks in a speech to the European Parliament in Strasbourg on Wednesday.
"I hope... that the government of the Russian Federation will not conclude that the only answer to terrorism is to increase the power of the Kremlin," he said.
A day earlier Mr Powell said that he wanted to discuss the measures with Moscow.
On Monday Russian President Vladimir Putin announced a sweeping overhaul of the way Russia is run, in the wake of a series of bombings and deadly attacks on civilians.
Mr Putin said strengthening central government control was a necessary part of the fight against terrorism, following the siege of a school in Beslan, southern Russia, in which hundreds of people died.
Speaking to reporters at a meeting of former Soviet states in Kazakhstan, Mr Lavrov said Washington had no right to impose its own model of democracy on others.
The reforms were, he said, being applied within the framework of the Russian constitution and he pointed to the "strict measures" introduced by the US after the 11 September 2001 terror attacks.
"We, for our part, do not comment on the US system of presidential elections, for instance," he added.
Mr Powell told Reuters news agency that Moscow should balance the need to go after terrorists with a commitment to the democratic process.
"It would be not the best course of action to move in a direction which [would] be seen by the international community as moving toward the rear with respect to democratic reforms," he said.
State department spokesman Richard Boucher had also urged Russia to "strike the right balance", while expressing Washington's solidarity with Moscow in the fight against terrorism.