New Australian Covid-19 cases dipped on Sunday as testing slowed over a holiday weekend, but remained well over 30,000 and hospitalisations rose further in New South Wales as concerns grow about potential strains on the national health system.

Newly diagnosed cases in New South Wales, the most populous state, dropped to 18,278 from 22,577 the day before as the number of tests conducted on New Year's Day dropped by a quarter, health department figures showed.

But hospitalisations...