Tesco said it was taking "another step in the right direction" after its UK like-for-like sales fell by 1.3% in the first quarter of the financial year.
The supermarket giant said the results were an improvement on the 4% fall in the same period last year and a 1.7% decline in the previous quarter.
Tesco chief executive Dave Lewis said: "Whilst the market is still challenging and volatility is likely to remain a feature of short-term performance, these first quarter results represent another step in the right direction."
Sales in Ireland fell by 4.4% - compared to 5.6% a year ago - while Asian revenue dropped by 3%, a slight improvement on the 3.2% fall in first quarter of last year.
Tesco said separate figures from Kantar Worldpanel had also shown that 180,000 more customers shopped at the supermarket in the 12 weeks to 24 May.
Mr Lewis said: "We set out to serve our customers a little better every day and the improvements we are making are starting to have an effect.
"We are fixing the fundamentals of shopping to win back customers and relying less on short-term couponing.
"These improvements have come during the restructuring of our office and store management teams, which testifies to the focus, skill and commitment of colleagues across the business."
The results come as a lively Tesco annual shareholder meeting is expected today amid investor concern over its chairman and the pay-offs of its departed chief executive.
Shareholder body Pirc recommends that investors vote against the supermarket's remuneration report at the London meeting which allowed it to hand a £1.2 million pay-off to former boss Philip Clarke - on top of £764,000 in salary until mid-January.
Mr Clarke was given the leaving pay-off in February, despite the group's financial woes, while former finance director Laurie McIlwee was also paid about £1 million on leaving in addition to salary payments.
Tesco said it plans to claw back the leaving payment if it finds there was gross misconduct following the discovery of an accounting black hole.
But Pirc said: "Such service payments are particularly concerning as the track record of these two executives at the head of the company was particularly poor."