Nov 4 (Reuters) - Woolworths Group Ltd said on Wednesday first-quarter sales surged 12% as coronavirus lockdowns boosted demand for household essentials but Australia's biggest grocery chain expects costs to remain elevated this year.

Sales were driven by increased demand for food supplies and cleaning products from shoppers in Australia's second-most populous state of Victoria, which has been under a lockdown since July to combat a second wave of the outbreak.

Chief Executive Brad Banducci told analysts in a conference call he expected sales and costs to "remain elevated" for the rest of the year as customers spend more time at home, travel less and embrace e-commerce.

"Given 2020 so far, it would be surprising if there weren't some challenges that lie ahead," Banducci said, adding that costs are expected to rise due to steps to keep stores and distribution centres COVID-19 safe.

Total group sales for the country's biggest supermarket operator came in at A$17.85 billion ($12.79 billion) for the 14 weeks to Oct. 4, up from A$15.90 billion a year earlier.

Woolworths' sales for the quarter were ahead of smaller rival Coles Group, which posted a 10.5% growth in sales last week.

However, closures in Victoria and restrictions in other states continued to hurt sales at the company's hotels division, with total sales declining by 33.2% from a year earlier to A$313 million.

The results sent Woolworth shares lower, as investors focused on the prospect of higher costs. They stood down 0.80% in mid-day trade while the benchmark index was 0.60% lower.

The company, which has been paying back-store staff after acknowledging widespread underpayment, added that A$164 million was paid during the quarter to remediate staff for salary payment shortfalls. ($1 = 1.3955 Australian dollars) (Reporting by Renju Jose in Sydney and Shruti Sonal in Bengaluru; Editing by Vinay Dwivedi and Ana Nicolaci da Costa)