David Cameron has received a reprimand from the official statistics watchdog over his claim that the government was "paying down Britain's debts".

The prime minister's assertion in last week's Conservative party political broadcast tiggered a furious complaint by Labour, which described his comments as "deliberately misleading" as the debt was actually rising.

Chair of the UK Statistics Authority, Andrew Dilnot, confirmed on Friday that public sector net debt has risen from £811bn in 2010 when the coalition took office to £1.1tn at the end of last year.

Responding to Labour's complaint, Dilnot said it was important that politicians distinguished correctly between accumulated debt, and annual public sector borrowing – which has come down under the coalition.

"It is clearly important for all parties to public debate in this area to understand the relevant statistical definitions and to distinguish changes in the level of debt outstanding from changes in borrowing per period, and to reflect these in their communication of the statistical trends involved," he wrote.

"Public sector net debt is a measure of how much the UK public sector owes at a given time. Public sector net borrowing is the difference between total accrued receipts and total accrued (current and capital) expenditure over a specified period; this measure is frequently used by commentators to summarise the extent of any public sector 'deficit'."

He added that he was sending a copy of the letter – with accompanying graphs setting out the relevant data – to Cameron's chief of staff, Ed Llewellyn.

The shadow chief secretary to the Treasury, Rachel Reeves, said: "It is hugely embarrassing for David Cameron that he has had to have the difference between borrowing and debt explained to him by the chair of the UK Statistics Authority.

"Now that his false claims have been exposed, it's time the prime minister stopped deliberately misleading people about his economic record."