South Korea has raised its virus alert level to the highest red as the number of coronavirus cases spiked to 604 and the death toll hit six.

More than half of the cases are linked to the secretive Shincheonji Church of Jesus in the south-eastern city Daegu, the epicentre of a community outbreak that has now affected all of the country's eight major cities and nine provinces.

President Moon Jae-in said the outbreak has reached a watershed moment, and raising the alert to the highest level will allow the government to cope with the crisis at a national level and strengthen its overall response system.

He said the next few days will be crucial: "The situation is grave, but we can overcome it. Trust and cooperation is the way to win this battle against the virus."

The coronavirus originated in the Chinese city of Wuhan and has now claimed more than 2,400 lives and infected more than 78,900 people, mostly in China.

In South Korea, red is the highest of four alert levels. Last activated during the H1N1 swine flu epidemic in 2009, the red alert level will allow the government to demand school closures, cancel mass events and set up a task force to take legal action to stop the virus from spreading.

The government will push for measures to prevent infections within hospitals, and medical teams will be empowered to test suspected patients regardless of their travel records. Prime Minister Chung Sye-kyun is also slated to head a new disaster countermeasures team that will oversee efforts to curb the spread of the virus.

The reopening of all schools will be pushed back a week to March 9.

Meanwhile, the Korea Centres for Disease Control and Prevention has quashed rumours that the country is running short on medical supplies to treat coronavirus patients. It said the country will keep a stable supply of medicine and is now conducting up to 6,000 tests a day.

Of the 169 new cases reported yesterday, 95 were linked to the Shincheonji church.

This brings the total cases related to the church to 329, but the figure is expected to rise further as more than 1,200 members - out of about 9,000 under self-quarantine - are showing flu-like symptoms.

It is still not known how the virus spread so rapidly from the church, after a 61-year-old woman who attended the church first tested positive last Tuesday.

The number of cases in Seoul reached 24 as of yesterday, while second-largest city Busan registered 13 cases. Among the new cases announced are a 16-month-old baby from Gimpo city, west of Seoul, and a four-year-old girl from Daegu.

Three deaths were announced yesterday - a 56-year-old woman from Daegu, and a 59-year-old man and a 57-year-old man, who both caught the virus while warded at Daenam Hospital in south-eastern city Cheongdo.