BRASILIA, Jan 28 (Reuters) - Brazil reported a record primary budget deficit of 743.1 billion reais ($138 billion) last year, the Treasury said on Thursday, as crisis-fighting expenditure saw total outgoings surge by a third and the economic slump hit revenues.

While the annual deficit was a runaway record, both in nominal terms and as a share of gross domestic product, it was below the government's last official estimate of 831.8 billion reais and below indications from Treasury officials that it could be just under 800 billion.

The Treasury said the deficit last year was a record 10% of GDP. That was less than the 11.5% forecast by the government last month. The 2019 primary deficit was 95 billion reais.

Treasury Secretary Bruno Funchal said 2021 would again be "extremely challenging", but insisted that the government would not break the spending cap, its key fiscal rule that limits public spending growth to the previous year's rate of inflation.

"It will be an extremely complex exercise, but one in which we must maintain fiscal discipline and contain expenditure," Funchal told reporters in an online news conference.

December's deficit excluding interest payments came in at 44.1 billion reais, bigger than the 35.7 billion reais median forecast in a Reuters poll of economists.

Net revenue in December slumped by more than a third in real terms to 131.6 billion reais from the same month a year earlier, while net revenue over the calendar year fell 13% in real terms to 1.47 trillion reais, the Treasury said.

Spending in December was 18.7% lower than the year before at 175.7 billion reais. But over the year, spending surged 31% in real terms to 1.95 trillion reais, almost entirely due to measures aimed at cushioning the COVID-19 blow to individuals, businesses and local governments, the Treasury said.

Last year, primary expenditures on tackling the crisis totaled 539.6 billion reais, of which 293 billion reais went on the emergency income transfer program to the poor that expired on Dec. 31. ($1 = 5.40 reais)

(Reporting by Jamie McGeever and Gabriel Ponte Editing by Alison Williams)