The UK's fourth-largest supermarket said like-for-like sales, excluding fuel, rose 0.7% in the three months to 1 May compared with a year earlier.
Morrisons said prices were down 2.6% from a year earlier as the supermarket price war continued.
Chief executive David Potts, who has now been in charge for a year, said there was "still much to do".
But he added he was encouraged by the progress being made by the company following a long period of declining sales and profits, which led to the resignation of former chief executive Dalton Philips at the start of last year.
"Customers are responding and satisfaction levels remain ahead of last year. We are of course pleased with a second consecutive quarter of positive like-for-like sales, which demonstrates our aim to stabilise trade is taking effect," he said.
Morrisons said it was helped by a 17% rise in sales from its Food to Go range, which includes freshly-made sandwiches.
Total sales fell 1.8% after Morrisons closed unprofitable supermarkets and sold its convenience stores.
Shore Capital analyst Clive Black said Morrisons had taken another step forward under Mr Potts, adding the supermarket was on a journey that was "taking the business to a better place for investors in our view".
"If Morrisons sustains robust ongoing trading and if industry conditions remain rational, albeit demonstrably competitive, then there may yet be scope for us to consider nudging up our pre-tax profit forecasts; when was the last time that such a comment was made about this company?" he added.
Morrisons shares rose 1.9% to 191.1p in early trading.
The figures from Morrisons come a day after Sainsbury's reported a fall in annual profits as a result of lower food prices.
Food price deflation has been prompted, at least in part, by intense competition between the "big four" supermarkets and so-called discounters such as Aldi and Lidl, which have been gaining market share in recent years.
Sainsbury's said underlying profits, which strip out one-off charges, fell to £587m for the year to 12 March. That was down from £681m in the previous year.
In March, Morrisons reported underlying pre-tax profits of £242m in the year to 31 January, down from £345m a year earlier.
Morrisons supermarket has reported a second quarter of rising sales as it continues to cut costs and prices.