* Australia reports 35 new COVID-19 cases
* Australia's COVID-19 on course for restrictions to ease
* Most populated state to allow bigger crowds at events (Recasts with national toll, adds quote from Victorian premier)
By Renju Jose and Colin Packham
SYDNEY, Sept 17 (Reuters) - Australia on Thursday reported its lowest one-day rise in new COVID-19 cases in nearly three months, as states said restrictions imposed to slow the spread of the virus will be further relaxed.
Australia said 35 cases of COVID-19 have been detected in the past 24 hours, the lowest one-day rise since June 24.
Victoria state - Australia's COVID-19 epicentre - accounted for the bulk of the new cases, with 28 people diagnosed with the virus in the past 24 hours.
"It is a fantastic outcome and a tribute to the hard work, sacrifice and contribution every single Victorian is making and I want to say thank you," Victoria state Premier Daniel Andrews told reporters in Melbourne.
The result in Victoria will buoy hopes that residents in Melbourne will soon be granted additional freedoms after more than six weeks under a strict lockdown.
Melbourne is on an extended hard lockdown until Sept. 28. If at that point the two-week average number of infections is below 50, which it currently is, then restrictions will be eased.
Restrictions in regional Victoria were relaxed earlier this week. Residents there can now have outdoor gatherings of up to 10 people, and cafes will be able to seat up to 50 people outside.
Australia's most populated state, New South Wales (NSW) said it had detected five new cases of COVID-19 in the past 24 hours, with two people already in hotel quarantine.
With confidence growing in NSW, state Premier Gladys Berejiklian said restrictions on crowds at sporting stadiums and venues will be eased. Venues will now be allowed to operate with a 50% capacity, double the previous constraint.
Australian states, Queensland and Western Australia both recorded one case each of COVID-19.
Australia has now recorded nearly 27,000 COVID-19 infections and 832 deaths. (Reporting by Renju Jose; Editing by Muralikumar Anantharaman, Tom Hogue and Michael Perry)