The lower house of parliament said in a statement that the resolution, which linked more U.S. aid to the withdrawal of troops, was an attempt to interfere in the internal affairs of Russia and Estonia.
"The fact that the U.S. Senate passed a resolution saying Russia will not get additional economic aid if it does not withdraw its troops from Estonia before Aug. 31 is seen as a move directed at the disruption of efforts to establish good neighborly relations between Russia and Estonia," it said.
Russia has pulled its forces out of Lithuania and has agreed to quit Latvia by the end of August.
But it has no deal with Estonia and has linked the removal of its 2,500 troops to the treatment of Russian-speakers and the rights of Russian military pensioners in the Baltic republic.
The U.S. move undermined relations between Russia and the United States, said the Duma statement which was passed by 228 votes to 14.
Vladimir Lukin, chairman of parliament's foreign affairs committee, was quoted by RIA news agency as saying the Senate resolution was "either stupid or provocative."
Russia and Estonia should be left in peace until the end of the month to sort out the withdrawal, he added.
Estonian leaders called this week for the international community to press Russia to keep to the Aug. 31 deadline.
The head of the Foreign Ministry's department for international humanitarian and cultural cooperation, Vyacheslav Bakhmin, was quoted by RIA as saying there was no doubt the troops would be pulled out.
"The question of the date is not a question of the withdrawal of the troops in principle," he said.
But he added that "fixing a precise timetable is a matter for the two states," and that it was not advisable for Russia to pull out by Aug. 31 while bilateral problems were unresolved.
The U.S. Senate's vote was an amendment to a foreign-aid bill which provides $839 million in aid for Russia and the other former Soviet republics.
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