David Cameron has issued his strongest declaration that climate change is man-made when he said it was one of the most serious threats facing Britain and the rest of the world.

The prime minister, who appeared to be wary in recent weeks of drawing a direct link between the effects of industrialisation and climate change, issued his unequivocal statement after Ed Miliband suggested he was unwilling to take tough action.

Cameron replied: "I believe man-made climate change is one of the most serious threats that this country and this world faces. That is why we have the world's first green investment bank here in Britain.

"That is why, unlike 13 wasted years of Labour, we are building the first nuclear power station for 30 years in our country. That is why we have cut carbon emissions emitted by the government by 14% since we came to office.

"That is why we have set out, year after year, carbon budgets in this country. They talk a good game about it but it actually takes people to come in, govern effectively and deal with it."

Cameron's remarks were immediately welcomed by green Tories, some of whom had feared the government was losing interest in combating climate change. Greg Barker, the climate change minister, tweeted Cameron's remarks and added: "Great to hear PM lauding the coalition's real achievements on climate change at #PMQs #RealGreenDelivery."

Recently, the prime minister privately reassured green Tories he was still committed to tackling climate change after being quoted by a minister as saying he wanted to get rid of the "green crap" on energy bills. But he said the government had to act cautiously as Britain recovers from the downturn.

George Osborne, who was criticised by green Tories in 2011 when he said Britain should not cut its carbon emissions at a faster rate than its EU partners, prepared the ground for the PM's remarks when he said last week he accepted climate change was man-made. But the chancellor told business leaders in Hong Kong it should be tackled in "as cheap a possible way".

Miliband said the PM's remarks were "excellent" but named a number of ministers who had questioned the need to tackle environmental change. The Labour leader quoted the environment secretary, Owen Paterson, as saying: "People get very emotional about this. People should just accept the climate's been changing for centuries."

Miliband quoted the energy minister Michael Fallon answering a question about climate change: "You are not going to draw me on that. I haven't had time to get into the climate change debate."

The Labour leader asked Cameron: "Is he happy to have climate change deniers in his government?"

Cameron said: "The most serious form of denial we have today in Britain's politics is the reality deniers of the party opposite. What is their plan for their deficit? Nothing. What is their plan for welfare reform? Nothing.

"What is their plan for long-term investment because that is what climate change requires? Long-term investment like high-speed rail, long-term investment like nuclear power, long-term investment like fixing our economy. That is what this government is doing. All he does is get up and deliver a lot of hot air."