Sweden's King Carl XVI Gustaf on Sunday urged Swedes to refrain from Easter travels to loved ones in a bid to curb the spread of COVID-19, as the death toll rises in one of Europe's few countries not in lockdown.

Sweden, whose softer measures to combat the spread of the new coronavirus have drawn criticism both at home and abroad, on Sunday reported 6,830 confirmed cases of the illness and 401 deaths.

That is up from 3,700 cases and 110 deaths one week earlier.

The figures are likely much higher in reality, as only patients admitted to hospital and health care personnel are being tested for the virus.

In stark contrast to its Nordic neighbours and much of Europe, Swedes are still able to move about freely though they are strongly advised to respect social distancing and to self-isolate at the first sign of symptoms.

People over the age of 70 and in risk groups have been advised to avoid contact with other people, and high school and university classes have been moved online.

But nursery and primary schools remain open, as well as cafes, restaurants and shops.

Among the stricter measures are bans on gatherings of more than 50 people and on visits to nursing homes.

Authorities have in recent days stepped up pleas to Swedes to stay home for Easter to slow the spread.

The holiday is "a time when we are keen to travel and perhaps spend time with family and friends. Many go to church," the king said in a televised address.

"But, this Easter, some of this will not be possible. We have to accept this. We have to rethink, prepare ourselves for staying home," he said.

The king, 74, and Queen Silvia, 75, who are considered at risk because of their age, have been self-isolating at a royal castle south of Stockholm, Stenhammars Slott.

Data on Sunday showed that 352 of the 401 deaths in Sweden were among those over the age of 70.

A third of the country's municipalities have confirmed or suspected cases of the new coronavirus in nursing homes, according to public broadcaster Swedish Radio.

Prime Minister Stefan Lofven has urged Swedes to take individual responsibility to slow the spread of the virus, as public health officials have expressed scepticism about the viability of lengthy lockdowns.

Critics have meanwhile called for more stringent measures.