The island will not know if community transmission of the coronavirus has started until more test results come in, the Premier said tonight.
But the Premier said he was “certain” that there were returning Bermudians who had flown in recently from the UK who carried the virus that causes Covid-19.
He emphasised the need for anyone in quarantine to obey the conditions and stay at home.
Mr Burt added that isolation was a step up from quarantine, which was imposed on people who displayed symptoms of the illness.
If someone under quarantine falls ill with Covid-19, others in their household will have to be quarantined and the sick member would have to be isolated.
Mr Burt warned viewers: “If you even feel a tickle in your throat or a cough, stay home.
“Some of the symptoms of this virus are incredibly mild. Someone described it as like feeling hung over, and the next day they felt fine.
“It depends on how your immune system is. But stay home.”
Mr Burt said in an online address that “by and large, Bermudians are being very good with obeying quarantine” since the island's partial lockdown was imposed this week.
Police conducted checks at licensed premises last night and today to enforce restrictions imposed in the wake of the island's first two confirmed cases of Covid-19.
Mr Burt revealed that about four Bermudians were repatriated on the Delta flight that arrived this afternoon to evacuate US citizens who wanted to return to the United States.
There are about 20 Bermudian students who have travelled through areas with Covid-19 in quarantine in hotels tonight.
Mr Burt also answered questions from the public submitted online in a video a video update on the island's Covid-19 status.
He said a curfew was not out of the question.
Mr Burt added: “If circumstances require, the Government will not hesitate to take actions necessary.
“I think actions we have taken to this point are certainly proportionate.”
One viewer said they had decided to work from home in line with Government advice, but were told by their employer that they needed a doctor's certificate.
Mr Burt said anyone asked to produce a certificate should e-mail him at firstname.lastname@example.org.
He added: “We will make sure that private business is spoken to.”
He said anyone with evidence of price gouging by store owners should also contact him and that complaints would be “followed up and prosecuted”.
Mr Burt added he had gone shopping earlier today and that there was no need to panic buy because stocks would not run out.
He said that people should pay attention to official sources and not spread misinformation.
Mr Burt told the public they should “maintain social distancing, and make sure you are not touching or in contact with other persons”.
There is now coronavirus hotline from 9am to 9pm on 444-2498.
Mr Burt said anyone stuck at home and unable to get supplies should call the hotline.
Another viewer asked if people failed to self-quarantine or held large gatherings would be punished.
Mr Burt said: “Yes and yes, no question about it.”
He advised people who witnessed breaches of the rules to “feel free to call the police”.
Mr Burt said field hospitals were an option if the King Edward VII Memorial Hospital became overburdened — but that he did not think that would happen.
He added that things would probably not return to normal on April 6 when the restrictions imposed this week came to an end on April 6.
But he said the island would be in a better position to assess would come next.
Mr Burt explained: “If we have verified community transmission that we cannot crack down on, we will have to take more drastic action.
“So it is important for us not to get to that place.”
Further updates will be given tomorrow after an Emergency Measures Organisation meeting, expected to be held around 6pm after the Cabinet met at 3pm.
Mr Burt thanked all the island's front line workers for their efforts to “make sure Bermuda comes through this crisis”.
He said: “We have responded well and we will continue to respond well as long as we have a spirit of unity.”