Dave Prentis, the general secretary of Unison, a union that represents many public service workers, nonetheless told the Press Association news agency that Mr. Cameron’s speech was “a chilling attack on the public sector, public sector workers, the poor, the sick and the vulnerable, and a warning that their way of life will change.”

The prime minister laid the blame for the situation squarely on what he called “reckless” spending by the Labour government, which was in power for 13 years before being defeated in last month’s election. He said that as the financial crisis was “Labour’s legacy,” so, too, would be the spending cuts.

Labour argued that spending would help stimulate the economy, Mr. Cameron said, “conveniently forgetting that if you start with a large structural deficit, ramping up spending even further is likely to undermine confidence and investment, not encourage it.”

Details of proposed spending cuts have not been public. The chancellor of the Exchequer, George Osborne, plans to set out the principles underlying his spending plans on Tuesday and to announce an emergency budget June 22.

Mr. Cameron said the cuts would come after wide consultation with members of the British public, driving home a recurring theme in his election campaign that “we’re all in this together.”

“It is precisely because these decisions are so momentous, because they will have such enormous implications, and because we cannot afford either to duck them or to get them wrong that I want to make sure we go about the urgent task of cutting our deficit in a way that is open, responsible and fair,” he said.

He said the financial situation had been worsened by the sovereign debt crisis in Europe. “The global financial markets are no longer focusing simply on the financial position of the banks,” he said. “They want to know that the governments that have supported the banks over the last 18 months are taking the actions to bring their own finances under control.”

As a cautionary tale, he mentioned Greece, where profligate spending led to a huge budget deficit and a downgrading on financial markets. While Britain’s economic position is stronger than Greece’s, he said, “Greece stands as a warning of what happens to countries that lose their credibility, or whose governments pretend that difficult decisions can be avoided.”