The Prime Minister said it would "foolish" to leave the country defenceless at a time when the "highly unpredictable and aggressive" regime in North Korea was developing ballistic missiles which could eventually threaten Europe.
The prime minister visited HMS Victorious after its return from patrol
His comments came as the United States said that it was moving an advanced missile system to the Pacific island of Guam as Pyongyang continued to ratchet up the rhetoric against South Korea and its American ally.
The Liberal Democrats are opposed to plans to renew the nuclear facility.
Writing in The Daily Telegraph, Cameron said such "evolving threats" underlined the need for the UK to maintain the ultimate deterrent.
"We need our nuclear deterrent as much today as we did when a previous British Government embarked on it over six decades ago. Of course, the world has changed dramatically. The Soviet Union no longer exists. But the nuclear threat has not gone away," he said.
"In terms of uncertainty and potential risk it has, if anything, increased."
Cameron said that Iran was continuing to defy the will of the international community over its nuclear programme while North Korea may already be building a nuclear arsenal.
"The highly unpredictable and aggressive regime in North Korea recently conducted its third nuclear test and could already have enough fissile material to produce more than a dozen nuclear weapons," he said.
"Last year North Korea unveiled a long-range ballistic missile which it claims can reach the whole of the United States. If this became a reality it would also affect the whole of Europe, including the UK."
He went on: "Does anyone seriously argue that it would be wise for Britain, faced with this evolving threat today, to surrender our deterrent?
"Only the retention of our independent deterrent makes clear to any adversary that the devastating cost of an attack on the UK or its allies will always be far greater than anything it might hope to gain."
His comments underline the Conservatives commitment to a like-for-like replacement for the ageing Trident submarine fleet while their Liberal Democrat coalition partners are seeking a cheaper alternative.
The future of Trident is also likely to feature in next year's looming Scottish independence referendum campaign, with the SNP insisting that it would not allow nuclear missiles to be based in an independent Scotland.
For Labour, shadow defence minister Kevan Jones said it was "absolutely right and necessary" for the UK to retain an independent nuclear deterrent, but it must take into account the costs involved.
"World events demonstrate that in an unpredictable era our country needs the ultimate security guarantee," he said.
"The precise nature of the deterrent must be judged on meeting military capability requirements and cost."
Lib Dem MP Sir Malcolm Bruce said he was concerned about funds being diverted away from conventional military equipment to pay for Trident.
"We do accept the case for a nuclear deterrent and we are not in favour of unilateral disarmament," he told Sky News.
"We are saying we shouldn't replace Trident on a like-for-like basis but we are looking at alternative nuclear deterrents once Trident has passed its sell-by date."
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