Group like-for-like sales grew 1.5 per cent in its third trading quarter, with UK like-for-like sales growing even faster, at 1.8 per cent.
The supermarket said it is on track to deliver at least £1.2bn in operating profit across the group.
Sales in the vital six-week Christmas trading period grew 0.3 per cent like-for-like, while growth hit 0.7 per cent in the UK. Food sales outperformed, with 1.3 per cent growth during the Christmas period.
Meanwhile, during the 19-week period ending on 7 January, UK volumes rose 1.1 per cent, and transactions were up 2.1 per cent.
However, international sales were more sluggish, with like-for-like growth of 0.6 per cent. The retailer blame "a more competitive environment in Poland".
Shares fell two per cent at the open of Thursday trading.
Why it's interesting
The Tesco results add another piece of the jigsaw to a strong start to the year in 2017 for the UK's supermarkets. Morrisons and Sainsbury's had already reported sales growth, with Marks & Spencer adding another positive result today.
The UK retail sector is bracing for the effects of inflation, but has so far come through unscathed as consumer spending held up following the June EU referendum.
Tesco warned deflation had eased as price increases begin to feed through and the so-called price war between the UK's largest supermarkets eased off. Many retailers and companies hedge for periods of six months, meaning they are protected in the short term from inflationary price rises after the Brexit-inspired devaluation of sterling in the second half of the year.
However, it's worth pointing out Tesco recently laid off 1,000 workers as it looks to make its distribution network more efficient.
Nicholas Hyett, equity analyst at Hargreaves Lansdown, said: “It’s five years since Tesco last took market share from its competitors. There are signs that the giant might be stirring once again, but a slow down over the Christmas period will leave many investors worrying whether the group can achieve sustained growth."
However, Richard Lim, chief executive of Retail Economics, suggested its medium-term prospects were stronger. He said: "Tesco’s turnaround continued to gather momentum with the behemoth posting impressive trading in the three months to Christmas.
"Its laser-like focus on the core UK food business through deeper price investment and further asset disposals has halted the loss of market share against the smaller but faster growing discounters. Non-food also saw impressive gains in both clothing and toys," he added.
What Tesco said
Dave Lewis, chief executive, said:
We are very encouraged by the sustained strong progress that we are making across the group. In the UK, we saw our eighth consecutive quarter of volume growth and delivered a third successful Christmas.
However, Lewis said international trading conditions were more difficult:
Internationally, we have continued to focus on improving our offer for customers in challenging market conditions.
Tesco has the goods for analysts, as it continues a week of good sales growth for UK supermarkets - but investors aren't so sure.