The data from market researcher Kantar Worldpanel showed Tesco's sales fell 3.6 percent in the 12 weeks to Oct. 12.

Though that performance was still the worst of Britain's so called "big four" grocers, it was Tesco's best figure since June and compared to a fall of 4.5 percent reported by Kantar in its September report.

Tesco's market share was 28.8 percent in the latest period, down from 30.1 percent in the same period last year.

The grocer's shares, which have halved over the last year, were up 2.5 percent at 0931 GMT (10.31 a.m. BST).

Tesco is due to publish interim results and an update on its probe into a 250 million pounds profit mis-statement on Thursday.

Analysts expect the firm to report sales at stores open over a year, excluding fuel and VAT sales tax, down about 6 percent for its second quarter to Aug. 23.

Tesco Chief Executive Dave Lewis said in a memo to staff last Friday that the firm's recent performance in food "has been one of our strongest for a very long time."

The Kantar data showed overall market growth of 0.7 percent, with like-for-like prices down 0.2 percent, pushing the grocery market into deflation.

"Extensive price cutting by some supermarkets in a bid to win the price war means that customers are saving on everyday items such as vegetables and milk," said Fraser McKevitt, Kantar's head of retail and consumer insight.

Of the big four, Wal-Mart's Asda was the winner with sales growth of 1.0 percent. Sales at Sainsbury's and Morrisons fell 3.1 percent and 1.8 percent respectively.

Among the discounters Aldi's [ALDIEI.UL] growth slowed slightly compared to recent months, but its sales were still up 27.3 percent. Lidl's [LIDUK.UL] sales grew by 18.1 percent.

(Reporting by James Davey, additional reporting by Paul Sandle, editing by Louise Heavens)