Sick and disabled people trying to claim a new benefit introduced by Iain Duncan Smith are facing "distress and financial difficulties" because of mismanagement by civil servants and the outsourcing firms Atos and Capita, a spending watchdog has found.

The National Audit Office discovered that the new personal independence payment, which will replace the disability living allowance, will cost almost three and a half times more to administer and take double the amount of time to process.

It has released a report into the new benefit as the government's £500m contract with Atos comes under increasing scrutiny. Disability minister Mike Penning described the contract with the benefits testing firm Atos as a "mess". Atos says that it wants to pull out of the contract early because of the death threats being made against its staff.

The department for work and pensions [DWP] had budgeted to pay £200m to administer the new benefit but pays Atos and Capita £127m to conduct face-to-face consultations or paper-based assessments.

The report shows that within six months of the introduction of PIPs in some areas of the north of England in April 2013, a backlog of 92,000 cases had built up, almost three times the number expected. The DWP had made decisions in only 16% of the expected number of cases, the report found.

Poor operational performance in the early stages of Duncan Smith's flagship programme have forced his department to stagger the full national roll-out of PIPs and increased the risk that it will not deliver value for money in the long term, said NAO head Amyas Morse.

Atos is singled out for criticism in the report. In October, the DWP postponed the rollout of the benefit because of fears that Atos could not reduce backlogs or manage higher volumes of cases.

Contractually, assessment providers should complete 97% of assessments within 30 days. By the end of October, Atos and Capita had completed 55 and 67% respectively, the report disclosed.

Claimants were waiting an average 107 days - and terminally ill patients 28 days - for a decision on their cases, an NAO report has found, rather than the predicted processing times of 74 days and 10 days respectively.

Delays in assessments have cut by £140m expected savings over the course of this parliament, with the DWP now forecast to save £640 million a year by 2015, rather than its prediction of £780m, said the NAO. However, the DWP still expects to achieve annual savings of £3bn by 2018/19, with 3.6 million claims assessed by 2018.

Each new PIP claim - worth between £21 and £134 a week to disabled claimants - costs an average £182 to administer, compared to £49 under the disability living allowance, said the report.

Morse said: "Claimants face long and uncertain delays and the department has had to delay the wider roll-out of the programme. Because it may take some time to resolve the delays, the department has increased the risk that the programme will not deliver value for money in the longer term."

The chair of the House of Commons public accounts committee, Margaret Hodge, said that the current backlog and delays in processing claims are unacceptable and will cause distress for vulnerable claimants.

"Once again we see the DWP under-performing – and we have little faith that costs will not increase down the line as it tries to get things under control.

"The Department needs to understand the causes of this backlog to develop a clear plan on how they are going to work with contractors to clear it, and ensure there are suitable processes in place to make sure this does not happen again," she said.

A DWP spokesman said that the NAO acknowledges this reform started on time and on budget, and that the department has reduced risk by rolling it out in phases. "This has enabled us to adjust our plans as we learn from the initial phases, well before the roll-out to the majority of existing Disability Living Allowance claimants next year," he said.