By Donny Kwok and Twinnie Siu

HONG KONG (Reuters) - Hong Kong's retail sales fell by double digits in September as coronavirus restrictions slammed the brakes on spending and tourism slowed to a trickle, but the decline was smaller than in August as infections slowed..

Sales plummeted 12.9% from a year earlier to HK$26.1 billion ($3.4 billion), government data showed on Monday, falling for the 20th month compared with a 13.1% decline in August.

In volume terms, retail sales slumped 13.4%, unchanged from the previous month.

"The business environment of the retail trade will remain challenging in the near term, as inbound tourism is unlikely to see a swift rebound and the labour market is still under pressure," a government spokesman said.

"However, with the stabilisation of the local epidemic and the recent relaxation of social distancing measures, local consumption sentiment is likely to revive further," the spokesman added.

For the first nine months of 2020, the value of total retail sales fell 28.7%, and 30% by volume, from the corresponding 2019 period.

The city's biggest retailer association estimated that 15,000 retail stores will close by the year-end, and urged landlords to extend rental relief. Business consultancy PwC has estimated retail sales will shrink 19.7% in 2020.

Hong Kong's long recession showed signs of easing in the third quarter helped by an improving Chinese economy, an easing of the COVID-19 outbreak and stronger financial market activity.

The economy shrank 3.4% in July-September from a year earlier compared with a 9.0% contraction in April-June, but increased 3% from the second quarter - the first growth after five quarters of decline, government advance estimate showed.

The city's tourist arrivals in September plunged 99.7% from a year earlier to 9,132 visitors, the tourism board said, compared with a drop of 99.9% in August.

Sales of jewellery, watches, clocks and valuable gifts, which depend heavily on mainland tourists, fell 25.7% in September versus a revised 37.4% plunge in August.

($1 = 7.7534 Hong Kong dollars)

(Editing by Jacqueline Wong)