Supermarket Asda has posted another sharp fall in sales, highlighting the uphill task the new boss faces as he attempts to turn the business around.

The chain – owned by US retail giant Walmart – reported a 5.8% plunge in like-for-likes sales, excluding petrol, in its third quarter to 30 September.

This comes on the back of a poor previous three months, when the group reported a 7.5% slump in sales, its worst quarterly performance on record.

Major supermarkets such as Asda have been locked in a five-year price war with discounters such as Aldi and Lidl, as cash-strapped shoppers hunt for lower prices.

New chief executive Sean Clarke, who took up the reins in July replacing previous boss Andy Clarke, has slashed the prices of everyday items as he bids to arrest falling sales at the group.

Clarke, the former boss of Walmart's China business, said: "We have lowered thousands of prices, improved hundreds of own brand products and invested in more hours for colleagues on the shop floor – so it's encouraging to see more customers shopping with us in stores and online."

Walmart Chief Financial Officer Brett Biggs said about the group's UK arm: "The key priority remains driving an improved customer experience and building sales momentum by simplifying the offer, improving product availability and making strategic investments in service and price."

High street retailers have been hit by the slump in the value of the pound since June's Brexit vote, which is putting pressure on suppliers to raise prices to cover mounting costs.

Respected Kantar Worldpanel data said Asda's sales dropped 5.2% in the latest quarter – the slowest decline for four months. But its market share slipped by one percentage point to 15.6%.

However, Asda is being outpaced by major rivals, with Tesco increasing its market share for the first time in five years after Kantar said its sales rose by 1.3%.

Morrisons also recently saw like-for-like sales lift 1.6% in the third quarter, boosted by strong trading at Halloween.