The Prime Minister said the military alliance should ensure it can respond quickly to threats in the wake of Moscow's "illegal" actions in Ukraine.
But he also called on Nato to agree how it will address the risks posed by an "unstable world of failed states, regional conflicts, terrorism and cyber-attacks" at next month's summit in Wales.
International pressure on Russia has intensified almost daily since the downing of flight MH17, with the loss of 298 lives.
Earlier this week the US and the EU announced a co-ordinated round of sanctions designed to hit the Russian economy. But even then Mr Cameron admitted that tougher actions might still be needed to stop Russia funnelling arms to separatists in Ukraine.
Earlier this week a damning report by the House of Commons Defence Committee also warned that the nuclear alliance was not adequately prepared for a potential threat from Russia.
In a letter to the leaders of Nato countries and alliance secretary general Anders Fogh Rasmussen, Mr Cameron asks the alliance to agree how to sustain a robust presence in Eastern Europe to reassure allies there.
Measures should include pre-positioning equipment and supplies in key locations, a new schedule of military exercises and the beefing up of Nato's Response Force of swiftly deployable land, air, maritime and special operations troops, the Conservative leader says.
He adds that the summit will take place at a "pivotal moment" in Nato's history.
"To the East, Russia has ripped up the rulebook with its illegal annexation of Crimea and aggressive destabilisation of Ukraine.
"To the South, an arc of instability spreads from North Africa and the Sahel, to Syria, Iraq and the wider Middle East."
The summit must agree how Nato should adapt to "respond to and deter" such threats, he said.
"While Nato has only ever sought to be a partner to Russia, not a threat, it is clear that Russia views Nato as an adversary.
"We must accept that the co-operation of recent years is not currently possible."
He also urges Nato country leaders to follow the UK and spend two per cent of GDP on defence, a move he said would signal that the alliance "means business".