Associated British Foods said the European retailer's like-for-like sales were 4% higher than a year ago in the period since September, with new selling space pushing the overall growth rate to 14%.
The improvement, which came despite unseasonably warm weather at the start of the period and strong comparatives in the previous year, helped AB Foods offset continued weakness at its sugar business.
The FTSE 100 company, which also owns leading food brands Ryvita, Twinings and Kingsmill, said overall profits for the six months to March 1 were expected to be in line with a year earlier.
It said: "A much lower profit from sugar will be offset by another excellent performance from Primark and encouraging results from grocery and ingredients."
Shares fell 2% today as AB Foods warned over the impact of sterling's recent strengthening on overseas earnings in the rest of this year.
Primark, which has around 160 of its 257 stores in the UK, achieved a 44% jump in profits to £514 million in its most recent financial year.
The new trading period has seen "excellent trading", including over Christmas.
AB Foods reported that the world sugar price has fallen to an unsustainably low level, putting further pressure on industry revenues and margins.
The decline reflects the end of EU sugar quotas in 2017, although the speed of adjustment has been faster than the company expected.
The mild winter resulted in its UK crop continuing to grow into the new year, with good beet quality and high sugar content.
Sugar production in the UK is now estimated at 1.3 million tonnes compared with 1.15 million tonnes last year.
AB Foods added that Twinings Ovaltine again performed well with strong sales growth for tea in the United States and the UK, and improved margins driven by higher volumes and factory efficiencies.
Kingsmill owner Allied Bakeries made progress in the highly competitive UK bread market as volumes and margins will be ahead of last year.