The new cases are in addition to the five identified yesterday, bringing the total infections for the current outbreak up to eight.
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WA Health confirmed the 25-year-old backpacker who tested positive after arriving in Perth from Queensland on December 12 has the Delta variant of concern, not the Omicron strain of the virus.
"All cases related to this outbreak can be assumed to also be Delta," WA Health said in a statement.
The state will bring in a hard border with both the Northern Territory and Tasmania from midnight tonight.
A total of 8606 tests were conducted in the last 24 hours at public and private COVID-19 testing clinics.
In a statement on Facebook Premier Mark McGowan said contact tracers are working to identify any further exposure sites.
In addition to the two locally acquired cases, WA also recorded two additional cases in hotel quarantine.