(Reuters) -Australian retailer Coles took market share from its biggest rival in the first quarter, cashing in on aggressive discounting and e-commerce gains, while Woolworths fights to rebuild consumer trust ahead of the crucial festive period.

Coles, the country's second-largest grocer, posted a near 4% jump in sales for the quarter ended September 28 to A$10.96 billion ($7.12 billion) on Thursday, outpacing Woolworths' 2.7% rise reported a day earlier.

The smaller firm has been expanding its range of cost-effective products to lure value-conscious customers on a hunt for bargains, powering 27.9% growth in e-commerce supermarket sales.

Its supermarkets unit reported a 4.8% rise in quarterly sales revenue to A$9.97 billion. Woolworths, which posted a 2.1% rise in quarterly sales at its Australian food division, has been cutting shelf prices on products in an attempt to win back shoppers.

Online sales also strengthened across Coles' liquor division, though the retailer said that market remained challenging.

The retailer added that early second-quarter trading showed sales growth running at a similar pace to the first quarter, underscoring steady momentum heading into the peak spending season.

Both Australian supermarket giants also face a broader competitive squeeze from the likes of German retailer Aldi and American giants Costco and Amazon, which have been intensifying investments in Australia.

Investors are watching for signs that a turnaround strategy from new Woolworths CEO Amanda Bardwell is gaining traction, with the Christmas quarter from October to December seen as a crucial test of her ability to win back shoppers.

Coles said the market continued to be competitive and it was focused on delivering value to customers over the festive season.

($1 = 1.5389 Australian dollars)

(Reporting by Sneha Kumar and Rajasik Mukherjee in Bengaluru; Editing by Anil D'Silva and Jamie Freed)