Government borrowing was higher than analysts' expectations in April after forecasts for company tax payments fell short of hopes.
The Office for National Statistics said borrowing, excluding support for state-owned banks, was £7.2bn in April.
That was down from £7.5bn last year but higher than analysts' forecasts of about £6,6bn.
The ONS also revised up its estimate of the amount borrowed in the financial year to March to £76bn.
That was £2bn more than its previous estimate, and £3.8bn above the prediction that had been made by the independent Office for Budget Responsibility (OBR), which produces forecasts for government.
The main reason for the lower figure was weaker-than-expected income from workers' national insurance contributions.
The ONS says annual borrowing has been falling in general since the peak reached in the 2009-10 financial year.
Last year's figure was £15.7bn lower than for the year before, and is half that borrowed in 2009-10.
The ONS said that total public sector net debt - excluding public sector banks - by the end of April stood at £1.596 trillion, the equivalent of 83.3% of gross domestic product.
April's figure was affected by less-than-expected tax income from companies. Corporation tax revenue fell 5.1% from a year earlier to £5.8bn.
The Chancellor, George Osborne, has laid out targets for borrowing, which he has pledged to continue to bring down.
Howard Archer, chief economist at IHS Global Insight, said: "The muted start to fiscal year 2016-17 will fuel doubts about George Osborne's ability to get the deficit down to £55.5bn in 2016-17.
"It will also likely fuel even larger doubts about his ability to meet his long-term objective of a surplus of £10.4bn in 2019-20, especially as he now has to cover the £4.4bn gap that has resulted from the dropping of the planned cuts to disability benefits."