CEO Ken Murphy said Tesco's market share was growing more than at any other time in the past two years.
Its market share rose 50 basis points to 27.6% in the 12 weeks to May 12 year on year, according to market researcher Kantar.
"Customers (are) switching to us from other retailers, shopping with us more often and with more in their baskets," said Murphy, adding that sales trends were in line with the group's expectations.
In contrast to Tesco's update, other recent UK retail data has been subdued, with wet weather and ongoing cost-of-living pressures denting consumer spending in May, particularly for larger ticket items such as furniture.
Tesco is benefiting from its strategy of matching the prices of discounter Aldi on key items, and the popularity of its Clubcard loyalty scheme, which provides lower prices for members.
These programmes are being financed by taking costs out of the business, with a further 500 million pounds ($637 million) of savings targeted for 2024/25.
Tesco said its total sales, excluding VAT sales tax and fuel, over the 13 weeks to May 25, its fiscal first quarter, were 15.3 billion pounds - up 3.4% on a like-for-like basis.
Tesco kept its forecast for retail adjusted operating profit, its preferred profit measure, of "at least" 2.8 billion pounds for its 2024/25 year, versus from 2.76 billion in 2023/24.
Its shares are up 15% over the last year.
($1 = 0.7850 pounds)
