SYDNEY, Jan 4 (Reuters) - The Australian and New Zealand dollars were pinned near two-week lows in holiday-thinned trade on Tuesday, weighed in part by the possibility that Australia"s surge in COVID-19 cases might make the central bank a bit more dovish. The Aussie last held around $0.7200. It has failed at several attempts to breach resistance around $0.7275 recently and has been testing support just below $0.7190. Australia"s COVID-19 cases touched a fresh pandemic high on Tuesday amid an Omicron surge in the eastern states that sent hospitalisations in New South Wales to a new peak. read more "We"ve seen a rapid surge in cases to more than 30,000 - the peak of previous waves, for context, in Australia was around 2,000 a day," said Goldman Sachs economist Andrew Tilton. Authorities seem confident that high vaccination rates will prevent serious illness, but strained testing infrastructure and shortages of rapid antigen kits are disrupting some businesses as workers isolate awaiting test results. The Reserve Bank of Australia had, before Christmas, sounded optimistic Omicron would not derail Australia"s economic recovery, but the speed of its spread has been unsettling. New Zealand reported its first community-transmission Omicron case on Tuesday, though total numbers there remain very low. The New Zealand dollar was steady at $0.6787 on Tuesday and it too has seen recent rally attempts stall around $0.6855. In the bond market, Australian government bond futures fell with the three-year bond contract down 5.5 ticks at 98.760. The 10-year contract dropped 6 ticks to a one-month low 98.220.