Britain will continue its plans to replace the Trident nuclear deterrent, the defence secretary has confirmed, as he moved to dispel speculation that he was less committed to the project.

Philip Hammond made clear that he would pursue the renewal plans, which could cost up to £25bn for four new submarines. His predecessor Liam Fox, who resigned last week, was strongly committed to Trident despite the project's huge cost, and the likely burden it will put on the already overstretched budget at the Ministry of Defence.

There had been talk at Westminster that Hammond might have a rethink, with experts noting that he had missed a vote in parliament on the need for Britain to have a "continuous at sea deterrence".

But in his first interview Hammond dismissed the doubters and said he was "absolutely committed" to Trident and always had been. He said he had only missed the parliamentary vote on the issue because he was "out on a visit on the route of the high-speed railway proposal".

"Had I been there I would have voted in favour," he said.

Fox announced in May that the government had approved "initial gate" – up to £7bn for the technical and design assessments needed for the renewal of Trident. The decision on "main gate" – the green light for construction of the submarines–was delayed until 2016 - after the next general election. This led to calls for ministers to consider reducing the number of submarines from four to three to cut costs, particularly as the £25bn does not include the money needed to buy new warheads.

The difficulties surrounding the renewal of Trident were underlined earlier this month in a report by Professor Malcolm Chalmers, of the Royal United Services Institute thinktank.

He said renewing Britain's nuclear deterrent was "the largest and politically most difficult procurement programme" for the MoD over the next 20 years, and predicted that unless the Treasury provided more cash to fund it, the department would have to make further drastic cuts to services and personnel.

Hammond insisted that the budget squeeze, and a redundancy programme that will mean up to 60,000 jobs being axed in the coming years, would not prevent Britain having a viable armed forces.

"We have had to make some serious budget cuts," he said. "My predecessor has successfully negotiated with the Treasury a settlement that will allow the UK to continue to project force abroad, to continue to have viable and sustainable armed forces in the future."

The cuts have hit all three services, and the start of the civilian jobs cull has now begun, with 3,000 staff leaving this month. Steve Jary, from the Prospect union, said: "By destroying its specialist capability, the MoD is putting the lives of troops at risk."