(Reuters) -Australia's Coles posted a rise in first-quarter sales, maintaining its lead over Woolworths, but analysts said the gap between the supermarket operators may be narrowing as Woolworths offers more discounts and better aligns inventory with demand.

Shares in Coles, the country's second-largest grocer, fell as much as 2.9% to their lowest since late August. Shares in its larger rival Woolworths climbed near 3%, hitting their highest level since September 1.

Coles reported a near 4% rise in sales revenue to A$10.96 billion ($7.12 billion) for the period ended September 28 on Thursday, outpacing Woolworths' 2.7% rise reported a day earlier.

A push towards e-commerce helped both supermarket operators achieve a rise in sales revenue. Coles posted 27.9% growth in e-commerce supermarket sales during the period, while Woolworths' e-commerce sales rose 13.2%.

After a soft start in the first quarter, Woolworths has ramped up investment in its stores to lift traffic and fend off intensifying competition, relying on deeper promotions and sharper pricing to win back shoppers.

Both retailers are locked in a battle for market share, using discounts and marketing firepower to appeal to cost-conscious consumers.

Woolworths on Wednesday reported an increase in sales at its Australia food retail business since the start of the second quarter, while Coles on Thursday flagged revenue growth at its supermarkets had remained steady over the same period.

Some analysts had held off passing judgment on Woolworths' update until Coles' release, viewing the back-to-back results as giving a clearer signal of which company is gaining the upper hand in Australia's grocery war.

Both companies are also facing a growing squeeze from global rivals such as Aldi, Costco, and Amazon, which continue to expand aggressively in Australia's retail market.

Jefferies analysts said it appeared Woolworths may have begun to close the gap with Coles from late in the first quarter, when it took action to invest in value and increase its focus on inventory.

At its annual meeting on Thursday, Woolworths CEO Amanda Bardwell said she was "cautiously optimistic" about trading in the second quarter, a peak period for supermarkets due to 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)