Comparative sales during the four weeks to December 26 grew 1.1 per cent with a "very strong performance" in the Christmas week with a 4.4 per cent improvement.
But the company – which plans to open 50 to 60 new stores this year as part of an "accelerated" expansion programme – said the overall trading environment remained difficult.
Same-store sales for the financial year as a whole increased by 0.8 per cent and the company said it expects annual results to be in line with forecasts.
In the Christmas week, the firm said it served 250,000 more customers than last year.
Greggs also said its savoury products were particularly in demand, with comparable sales up 10 per cent.
Meanwhile mince pie sales were boosted by the launch of a new Viennese version.
Chief Executive Ken McMeikan said : "I am very pleased with our sales performance, particularly over Christmas, in what has remained a challenging trading environment for the high street.
“We expect to report results in line with expectations when we make our preliminary results announcement on 18 March."
The Newcastle-based group – which currently has 1,419 stores – plans to open more shops in areas including the south west, north east Scotland and north Wales.