Adds details and CEO comments throughout, analyst comments in paragraphs 8-9

By Roushni Nair and Rishav Chatterjee

May 1 (Reuters) - Australia’s largest supermarket chain Woolworths WOW.AX said cost-conscious shoppers were increasingly looking for cheaper alternatives amid rising living costs, spurring its push into more private-label offerings, similar to rival Coles COL.AX.

Cost-of-living pressures loom as a key issue for Australians voting in a general election on May 3.

Woolworths, which sells more than one-third of Australian groceries, posted better-than-expected third-quarter sales on Thursday, as price cuts boosted volumes in its core grocery business.

Shares ended 1.2% higher at $31.94 on Thursday.

Woolworths' home-label brands remained popular among customers, especially in categories offering discounts of over over 40%, CEO Amanda Bardwell said on Thursday.

"We're seeing a lot of value-seeking across our grocery areas and that's where we're seeing an increasing number of products for own-brand perform particularly well," Bardwell told reporters on a call.

Group sales rose by 3.2% to A$17.31 billion ($11.09 billion) in the third quarter compared to A$16.77 billion the prior year. Own-brand and e-commerce increased by 5.7% and 15.7% respectively during the period.

Jesse Moors, portfolio manager at Spatium Capital, said the year-on-year growth in online sales was not a surprise given more people were opting to stay indoors, and "receiving the spending dopamine-hit via their mobile devices."

Analysts at Jefferies highlighted a stronger-than-expected third quarter for both Woolworths and Coles, suggesting an improvement in market conditions.

While the results showed resilience in a challenging retail landscape where cooling inflation has limited pricing power, Bardwell said customers remained concerned by rising living costs and managing budgets.

Woolworths has lowered prices on over 340 products, reducing them by an average of 1.2% on everything except fruit, vegetables and tobacco.

"Overall, our prices are competitive against our main competitors but there is this ongoing work we need to do," she told analysts on a conference call.

Smaller rival Coles reported an increase of 3.4% year-on-year in third quarter group sales, reflecting strong growth at its supermarket business on higher volumes.

Woolworths' Bardwell flagged that clothing continued to pose challenges at Woolworths' Big W operations, which runs discount department stores.

"Clothing sales were driven by spring summer clearance activity with a slower start to autumn winter, which has continued into April," Bardwell said.

($1 = 1.5613 Australian dollars)

(Reporting by Roushni Nair and Rishav Chatterjee in Bengaluru; Editing by Alan Barona, Shri Navaratnam and Rachna Uppal)

((Rishav.Chatterjee@thomsonreuters.com, Roushni.nair@thomsonreuters.com))