Russians react to Start vote
The State Duma - or lower house of parliament - appeared to be reacting to a similar resolution passed by the US Senate. A final vote on ratification is expected on 25 January, after which the treaty will go to the upper house for approval.
Applying a set of conditions is seen as a tit-for-tat response to US Republican moves to hedge the treaty signed by President Barack Obama.
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Hide AdKonstantin Kosachyov, head of Duma's foreign affairs committee, said: "The Russian Federation will treat the agreement with the highest degree of responsibility."
New Start would limit each country to 1,550 strategic warheads, down from 2,200.