The Department for Work and Pensions has come under pressure from Britain's biggest private employer to fundamentally change the terms of one of its flagship unemployment schemes following complaints that jobseekers are being used as taxpayer-subsidised labour in high street chains up and down the country.

Supermarket group Tesco said it has asked DWP officials to make the work experience scheme voluntary after thousands of angry customers wrote in and posted messages on Twitter and the company's Facebook site accusing the multinational of profiting from hundreds of thousands of hours of forced unpaid work.

Under the scheme, jobseekers work up to eight weeks for 30 hours a week in placements organised by job centre managers. These can take place in private businesses after the government changed the rules at the start of 2011. Before that, work experience placements were limited to two weeks and could only take place at charities and public bodies.

After the eight weeks those who have worked in store are promised no more than an interview. Companies have no obligation to have a job on offer before they enrol the unemployed on a placement. According to the latest figures 34,000 people were put through the scheme between January and November last year.

If jobseekers pull out of a placement after the first week they face having their benefits withdrawn.

In a statement from Tesco on Friday night, the company – which made £3.8bn in profits last year – said it wanted the scheme to be free from any sort of sanction.

"We understand the concern that those who stay in the scheme longer than a week risk losing their benefits if they drop out before the end of their placement," Tesco said. "We have suggested to DWP that to avoid any misunderstanding about the voluntary nature of the scheme, this threat of losing benefit should be removed."

Behind the scenes, DWP officials have been desperately attempting to shore up support for the scheme which David Cameron, Nick Clegg and George Osborne have personally championed. On Thursday, officials described claims that firms were thinking of withdrawing as "overheated nonsense", adding: "A vast number of businesses are involved in providing work experience schemes, including some of Britain's biggest names."

The government recently said it was extending the scheme to more than 100,000 placements a year. However, this has not stopped Sainsbury's, Waterstones and clothing giant TK Maxx announcing in recent weeks that they were pulling out.

Waterstones said it did not want to encourage unpaid work. Sainsbury's stressed the only back-to-work scheme it was engaging with was entirely voluntary and would try out benefit claimants for an actual job vacancy. The Guardian understands that other major high street chains are reconsidering their involvement.

Tesco said it had entered the scheme in good faith but had "felt uncomfortable" about being involved in a programme which was seen as compulsory. It said it had made its concerns known to senior departmental officials on Friday.

Tesco did not comment on what action it would take if the DWP refused to change the terms of the scheme. Any move would undermine ministers' previous stance on the importance of sanctions to reinforce personal responsibility.

"We would never offer longer-term work on an unpaid basis," a Tesco spokesperson said, adding: "We remain 100% committed to offering long-term, sustainable and rewarding paths into employment for thousands of young people.''

DWP officials said the sanctions were introduced for those who withdraw from a placement after the first week to protect employers from wasting time, but said they were "happy to discuss with employers whether this is warranted".

Chris Grayling, employment minister, said in a statement: "Our work experience scheme is voluntary and thanks to companies like Tesco and many others it has provided a route for literally thousands of young people to find their first job." He added: "The idea that providing work experience for unemployed young people is some kind of forced labour is utterly and completely absurd."

Lawyers who are bringing a legal claim against the department under the Human Rights Act legislation on forced labour, welcomed Tesco's move. Solicitor Jim Duffy from Public Interest Lawyers said: "Tesco, one of the main beneficiaries of the schemes, has now recognised that coercing people into unpaid labour will not solve Britain's unemployment crisis or empower Britain's 2.6 million unemployed. The government must now scrap these schemes and come up with individualised tailored approaches that will not only get people into work but will keep them there."