The lower house of the Russian parliament, the Duma, has voted to give initial approval to the Start nuclear arms pact with the US.
The treaty, aimed at reducing both countries' nuclear arsenals and allowing their inspection, was ratified by the US Senate on Wednesday.
There were hopes the Duma would give its full approval but officials decided that two more readings were necessary.
The pact must also be ratified by the upper house, the Federation Council.
Before MPs voted to back the treaty by 350 votes to 58, concerns were expressed in the Duma about two non-binding amendments that had been made by the Senate before ratification.
Russian Foreign Minister Sergei Lavrov said the amendments - committing the US to a missile defence system and modernising its nuclear arsenal - did not change the treaty as a whole.
He said US efforts to remove "future strategic-range non-nuclear systems" from the scope of the pact were "unacceptable".
The treaty will have to pass two more readings in the Duma in January after the winter break, before going to the Federation Council.
But Defence Committee chairman Viktor Zavarzin said the measure should not be rushed.
"We cannot be criticised for dragging out the ratification process of the treaty. In this process we do not have the right to make a mistake, we must weigh up everything," he said, quoted by Itar-Tass news agency.
Earlier, Russian President Dmitry Medvedev praised President Barack Obama for pushing the pact through the Senate.
The Senate approved the treaty by 71 votes to 26, after months of wrangling and over the objections of some top Republicans.
The New Start treaty, which will replace its lapsed predecessor, Start (Strategic Arms Reduction Treaty), was signed by the two presidents in April 2010.
It trims US and Russian nuclear arsenals to 1,550 deployed nuclear warheads - a cut of about 30% from a limit set eight years ago.
The treaty would also allow each side visually to inspect the other's nuclear capability, with the aim of verifying how many warheads each missile carries.
A previous inspection regime - part of the old Start treaty - expired a year ago.
In addition, there will be legally binding limits on the number of warheads and missiles that can be deployed on land, on submarines, and on bombers, at any one time.