Russian defence chiefs said last week that its missile shield will be much cheaper and more practical than the US scheme.
President Vladimir Putin pressed Lord Robertson of Nato to consider Moscow's proposal seriously.
Moscow's own proposals envisage the creation of a mobile anti-missile system, which could be deployed quickly to counter any potential threat.
Existing agreements
But a senior defence official said the shield would only be used as a last resort.
The BBC Moscow correspondent says Russia is hoping to win the backing of European Nato members.
France and Germany have already expressed interest in Moscow's proposed system, which includes:
Senior Defence ministry official Colonel-General Leonid Ivashov said the plan would abide by existing arms agreements.
Cheaper than America's
Russia, with an annual defence budget of $6bn compared with the US's $300bn, does not have the resources to develop a costly anti-ballistic missile system.
Western analysts say the Russian version may be a ploy to divide the US from its European partners, who are lukewarm about the NMD.
Russian defence chiefs said last week that its missile shield will be much cheaper and more practical than the US scheme.
Arriving in Moscow on Monday night, Lord Robertson said that Russia and Nato were building a "crisis-resistant relationship" which would allow them to deal with the "tricky issues" in the world.
Relations between Nato and Russia suffered badly during Nato's bombing of Yugoslavia two years ago.
BBC Moscow correspondent Steve Rosenberg says Lord Robertson's two-day visit comes at a time when Russia is adopting an increasingly hard line with the West.
Show of strength
Our correspondent says Russia has been trying to prove to the world it is still a force to be reckoned with.
It has sent nuclear-capable bombers close to foreign airspace during exercises, and launched three strategic missiles.
Russian defence chiefs have warned of retaliatory steps if Nato expands too close to Russia's borders.
In an attempt to provide an alternative to NMD Mr Putin last year offered to work with the US on a defence shield using smaller tactical rather than strategic missiles to shoot down incoming threats.
Russia is the only country in the world with a functioning ballistic missile defence system, which protects the Russian capital, Moscow.