Japanese rubber futures sank on Friday for a second day, marking their first weekly loss in four, as persisting worries about the Omicron coronavirus variant and weaker factory data in top buyer China weighed on sentiment. Osaka Exchange"s rubber contract for May delivery , finished 3.0 yen, or 1.2%, lower at 240.6 yen ($2.1) per kg. It booked a 2.3% weekly loss after three weeks of gains. The rubber contract on the Shanghai futures exchange for May delivery plunged 255 yuan to finish at 14,720 yuan ($2,311) per tonne, a two-week low. President Joe Biden laid out his strategy on Thursday to fight the Omicron and Delta variants over the winter, including free and insurer-funded at-home COVID-19 testing and new requirements for international travellers. [USN:L1N2SN18O] Activity in China"s services sector expanded at a slower pace in November amid rising inflationary pressures and continuing small-scale COVID-19 outbreaks, a private survey showed on Friday. [USN:ZRN003H3Q] "Rubber prices were under pressure due to worries over the Omicron effect and a slowdown of China"s economic growth, including falling automobile sales," a Tokyo-based dealer said. China"s auto sales fell in October for a sixth consecutive month, slumping 9.4% from a year earlier, industry data showed last month. [USN:L1N2S10CR] Rubber inventories in warehouses monitored by the Shanghai Futures Exchange rose 30.2% from last Friday, the exchange said on Friday. [USN:AZN01W23X] The front-month rubber contract on Singapore"s SICOM exchange for January delivery last traded at 173.0 U.S. cents per kg, down 0.9%. TOKYO, Dec 3 (Reuters) - ($1 = 6.3702 Chinese yuan) ($1 = 113.4100 yen) Reporting by Yuka Obayashi; editing by Uttaresh.V