It is "inevitable" more health workers will die from coronavirus, the UK's largest nursing union has said.
She said the circumstances of both deaths had to be reviewed and protocols for frontline staff examined.
England's chief nurse Ruth May has also raised fears over more deaths.
It comes amid reports that up to 30 nurses are off sick with coronavirus at Southend Hospital in Essex.
Ms Fyffe said there were still concerns about whether staff had the personal protective equipment (PPE) they needed "not just in the NHS - in the communities, in the care homes, in the hospices, wherever care is being provided".
The Department of Health and Social Care said a hotline was available for ordering PPE.
During the government's daily briefing on Saturday, Cabinet Office Minister Michael Gove said seven healthcare professionals have now lost their lives.
Ms Fyffe said nurses were unable to keep a safe distance from patients, adding: "People have forgotten that when you are a nurse... you are working with patients who are actually up close and personal.
"I do believe, sadly, it is inevitable we will see more nurses and other healthcare professionals die."
During Friday's government briefing, nursing chief Ms May paid tribute to Ms O'Rourke and Ms Nasreen, who were both mothers-of-three in their 30s and worked on the frontline in facilities in Margate and Walsall.
She added: "I worry there's going to be more [deaths]."
'Working round the clock'
Dame Donna Kinnair, chief executive of the Royal College of Nursing (RCN), said nurses were treating patients with coronavirus without any protection at all and putting themselves, their families and their patients at risk.
"We will not accept anything less than aprons, gloves and masks for all staff, in all settings," she added. "But that is a minimum."
She said the RCN had written to Prime Minister Boris Johnson at the end of March asking him to intervene.
A spokeswoman for the Department of Health and Social Care said: "We are working round the clock to make sure that our heroic frontline healthcare staff feel safe, and the full weight of the government is behind the effort to make sure PPE is reaching the frontline.
"We are working closely with industry, the NHS, social care providers and the Army.
Southend University Hospital NHS Foundation Trust said no-one was available to comment until Monday.