NATO needs to sustain a "robust" defensive presence in eastern Europe, Cameron wrote in a letter to the alliance's Secretary General Anders Fogh Rasmussen, and the 27 other NATO country leaders.
The North Atlantic Treaty Organization also needs to beef up its response force of rapidly deployable land, sea, air and special operations troops, he said.
With six weeks to go before Britain hosts the NATO summit in Newport, south Wales, Cameron said he wanted to use the meeting to agree a tougher policy towards Moscow, which would send a message that NATO member states would not be intimidated.
"To the south, an arc of instability spreads from north Africa and the Sahel, to Syria, Iraq and the wider Middle East.
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"So we must use the summit to agree how NATO should adapt to respond to and deter such threats; and to ensure the continued collective defence of all its members."
He said while NATO had 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 because of Russia's own illegal actions in NATO's neighbourhood and revisit the principles that guide our relationship with Russia."
NATO must agree on "long-term measures to strengthen our ability to respond quickly to any threat, to reassure those allies who fear for their own country's security and to deter any Russian aggression".
As NATO's combat operations in Afghanistan wind down towards the end of the year, he said the alliance had to consider how to support the country in the future and stop it from "once again becoming a safe haven for terrorists".
He also urged the 28 member states to meet the NATO target of spending two per cent of gross domestic product on defence, something Cameron said only four countries were achieving.