Russian lawmakers have voiced concern about Nato's eastward expansion to Moscow's doorstep.
Many deputies were angered by Nato's move
A resolution by the lower house of parliament, the Duma, said Russia may reconsider its defence strategy if Nato continued to ignore Moscow's interests.
It urged Nato members to ratify an arms treaty to restrict deployment of weapons near Russia's borders.
On Monday, the Baltic states of Latvia, Estonia and Lithuania joined the bloc together with four other nations.
The Duma's tough resolution was supported by 305 deputies, with only 41 voting against and also two abstentions.
The document said Nato's move eastwards contradicted a pledge to enhance the alliance's co-operation with Russia in counterterrorism, peacekeeping and other areas contained in an agreement signed in 2002.
It also warned that Russia may revise a promise to limit troop numbers in its Baltic enclave of Kaliningrad, and the northwestern Pskov region near Estonia, if Nato tried to change the military-political balance in the whole region.
"Common responses to modern global challenges don't require a build-up of weapons on the territories of Russia's neighbours," the resolution said.
The Duma said it would also recommend the government to strengthen Russia's nuclear deterrent and consider the deployment of additional troops on the country's western borders.
Earlier this week, the US ambassador to Nato, Nick Burns, said there was no sense of a crisis in relations with Russia over the expansion.
Mr Burns also said Nato had no intention of deploying substantial forces in any new member country.