A male resident at Newmarch House aged care died on Monday, meanwhile, taking the Caddens facility's toll to 15 and the NSW death toll to 45.
Some 37 of the 100-odd Newmarch House residents have tested positive to the virus.
"Two new cases were from staff members at Newmarch House and detected as part of the screening process that has been put in place," Dr Chant told reporters on Tuesday.
Anyone with respiratory symptoms should seek COVID-19 testing, she said.
Three new cases were recorded on Tuesday in NSW - the two Newmarch House workers and a health worker in western Sydney who did not work while infectious.
Federal Aged Care Minister Richard Colbeck on Monday said discussions were under way with some Newmarch House residents' family members to remove them from the facility.
He said it could be eight weeks before the facility is coronavirus-free.
Meanwhile, the Special Commission of Inquiry into the Ruby Princess cruise ship will begin its third round on Tuesday to help uncover the missteps of the ill-fated ship that has been linked to more than 20 coronavirus deaths and 600 infections across Australia.
The first two sittings included witness testimonies from the cruise ship's doctor Ilse Von Watzdorf and the hotel manager on board, Charles Verwall.
The hearings will run on Tuesday, Wednesday and Friday, with five new witnesses expected on Tuesday.
A seven-year-old schoolboy from Warragamba Public School in western Sydney was the sole new case of COVID-19 reported in NSW on Monday.
The school is now closed for intensive cleaning.
NSW has recorded 3035 COVID-19 cases, with 13 in intensive care.
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