The work and pensions secretary, Iain Duncan Smith, has been criticised by the UK's statistics watchdog for misusing figures to promote the effectiveness of the coalition's benefits cap on getting people into work.

In a press release issued by the Department of Work and Pensions last month alongside "ad hoc" statistics, Duncan Smith was quoted as saying "already we've seen 8,000 people who would have been affected by the cap move into jobs. This clearly demonstrates that the cap is having the desired impact".

However, in an open letter sent on Thursday, Andrew Dilnot, chair of the UK Statistics Authority, said this claim was "unsupported by the official statistics published by the department".

He added that the statistics used to support the statement had explicitly cautioned that the figures were "not intended to show the additional numbers entering work as a direct result of the contact".

Dilnot also criticised the two sets of figures released alongside the ministerial statement, saying they did not fully comply with the UK's codes of practices on statistical releases, with particular concerns around information on methodology and sourcing, and possible sharing of the data in advance with some media outlets.

The letter was sent in response to an official complaint sent by the TUC. The general secretary, Frances O'Grady, said the criticism showed the government's case on benefit reform was weak.

"Only people with weak arguments need to make up statistics," she said. "Of course we need a welfare system that guards against abuse, but this government is now causing real hardship and worry to many who have done nothing to cheat the system and are desperate to work.

"The secretary of state needs to apologise not just to parliament, but to the many who cannot find jobs, for misusing his department's statistics in this way."

The row also provoked an online petition on the change.org website calling on MPs to hold Duncan Smith's use of statistics to account, which has attracted more than 50,000 signatures.

The petition was started by two disabled activists, Jayne Linney and Debbie Sayers, who said "it is one thing to live with the physical challenges of a disability. It is quite another to hear lies and misinformation every day from our own government."

The DWP said the anecdotal responses of staff and claimants supported Duncan Smith's public statement.

"The secretary of state has long held the position that the benefit cap would have an impact on the behaviour of claimants," it said. "As the minister for employment made clear in a recent interview, DWP staff and claimants are telling us the cap is impacting behaviour and leading to those affected finally entering the world of work.

"It's important to remember that all those potentially impacted by the cap have been contacted by DWP staff who work with the unemployed day in, day out."

Another statement by Duncan Smith later in the month also drew criticism. The minister said around 1 million people have been stuck on benefits for at least three of the last four years "despite being judged capable of preparing or looking for work".

However, the figures cited also included single mothers, people who were seriously ill, and people awaiting testing.