Britain's statistics watchdog has issued a strong rebuke to ministers who rushed out figures last Friday purporting to show that 371,000 migrants were claiming welfare benefits.

Sir Michael Scholar, the head of the UK Statistics Authority, wrote on Wednesday to the work and pensions secretary, Iain Duncan Smith, telling him that the figures published were "highly vulnerable to misinterpretation". Duncan Smith responded by saying there were no plans to repeat the exercise.

Scholar said the figures should have been published as official statistics and not issued as "a research report". He said this would have prevented the employment minister, Chris Grayling, and the immigration minister, Damian Green, from issuing a political commentary ahead of their publication, as they did in a Telegraph article.

"These statistics are both highly relevant to public policy and highly vulnerable to misinterpretation," said Scholar. "There are important caveats and weaknesses that need to be explained carefully and objectively to parliament, and to the news media at the time of publication," he said.

The DWP research report was the first time a cross-analysis – matching benefit, border control and tax records – had been done on the number of people claiming working-age benefits who had been non-UK nationals when they first entered Britain.

The two ministers argued that the exercise was needed to ensure Britain did not have a system that encouraged benefit tourism. They announced that the 250,000 from outside Europe would all have their immigration status checked to ensure they were entitled to claim benefits.

Critics accused the ministers of scaremongering and said only 2% of the 9,000 cases sampled in the statistical exercise – 125 people – appeared to have no right to claim benefits. Most of the 371,000 had been granted British citizenship or the right to settle in the UK.

Scholar's letter seeks an assurance from Duncan Smith that such figures in future are published and handled as official statistics in line with Whitehall's code of practice.

Duncan Smith said his department's "ad hoc analysis" had been prepared by DWP statisticians to the appropriate professional standards. The report on their website had included all the relevant sources, caveats and limitations to the data.

"The department takes its obligations under the code of practice for official statistics very seriously and I note that no breach of the code took place," he said.

Duncan Smith said he noted Scholar's insistence that if the figures were published again they should be issued as national statistics. "However, we have no plans at present to repeat this analysis," he said.