Authorities have seen an increase in the number of people testing positive for COVID-19 after arriving on flights from other countries, including those not on Malta's amber list.
This week there were 14 so-called 'imported' coronavirus cases, up from just one last week.
Six were from Spain and France, which are on the island's amber list, where passengers have to show a certificate proving they are COVID-free or can be asked to take a test.
However, Charmaine Gauci said most people continue to contract the virus through friends, family and at the workplace.
The Superintendent of Public Health detailed the COVID-19 situation in Malta, which currently has the highest two-week death rate in the EU. Her weekly briefing came hours after two more people died with the virus.
During her briefing, she revealed that a third person died while being treated in Mater Dei's intensive care unit, bringing the death toll to 38.
"The mortality rate is high," she said. "In the first phase, we had only 9 deaths. Now, we have seen a number of deaths as a result of the outbreak in homes but we also had a number of deaths involving elderly in the community."
On Friday, authorities announced 44 new COVID-19 cases, from 2,252 tests and that 63 patients had recovered.
Watch the briefing live below
Less than ten per cent of the 434 active cases are being treated in hospital, Gauci said, with five in Mater Dei's intensive care unit, 17 in other wards and the remainder in hospitals in Malta and Gozo.
There have also been an increase in the number of cases in San Guzepp residential home for the elderly in Fgura, where 127 residents and 32 staff now have been infected.
In Simblija 15 residents have tested positive (they have started to recover and the situation is under control), in San Paolo three, in Casa Antonia two and in St Vincent De Paul, three residents. A ward there has been closed off and residents moved to other wards in isolation, Gauci said.
"This helps us stop the spread," she said. "We have also stepped up testing so we can identify more patients."
Seventeen people who were in the same ward as the three COVID-positive patients at the St Vincent de Paul have been quarantined, she said.
Where are people contracting COVID-19?
Gauci said that while there are sporadic cases, authorities have been able to trace most to particular clusters.
The majority of cases are family links, with 21 from family contacts this week. People are also contracting the virus at work. Authorities have identified five workplace clusters, resulting in 19 new cases.
A higher number of new cases have been traced to air travel than have been reported in previous weeks. She said that some of those who tested positive were on repatriation flights and had been in quarantine.
Asked whether Malta will be introducing the mandatory tests in light of the number of new cases, Gauci said those on the amber list are already being tested. She did not say whether mandatory testing will be introduced.
And there has also been an increase in cases in Gozo. While last Friday, Gauci said the island had just one case, there are 23 active cases there.
Most of this week's patients were aged 25-54, she said, but that some were aged between 85-90, one of the most vulnerable groups. The average age of a new patient is 45 years old.
Correction October 2: Casa Antonia currently has two active cases out of a total of 35 cases reported at the home in total.