The operator of a coronavirus-stricken cruise liner has warned that more people could die at sea unless its vessels are allowed to dock, accusing governments of “turning their backs” on thousands of people stranded at sea during the global pandemic.

Orlando Ashford, president of Holland America Line, called for a port to show “compassion and grace” by allowing passengers on the Zaandam cruise liner and its sister ship, the Rotterdam, back on land.

Four people have died, eight people have tested positive for Covid-19 and about 200 people are ill with flu-like symptoms on the Zaandam, which has hundreds of British, American and Australian holidaymakers on board, many of whom are elderly.

Both ships are travelling towards Florida but on Monday, governor Ron DeSantis said passengers cannot be “dumped” in his state and cast further doubt over whether ships would be allowed to dock, dismissing those on board as mostly “foreigners”.

A meeting of Broward county commissioners will take place on Tuesday to discuss whether the vessels should be allowed into port in Fort Lauderdale.

Several Latin American countries closed their ports to the Zaandam as the coronavirus outbreak developed on board and they refused emergency requests to medically evacuate critically ill patients, according to Ashford.

“We are dealing with a ‘not my problem’ syndrome. The international community, consistently generous and helpful in the face of human suffering, shut itself off to Zaandam leaving her to fend for herself.

“Nations are justifiably focused on the Covid-19 crisis unfolding before them. But they’ve turned their backs on thousands of people left floating at sea. Are these reactions based on facts from experts like the US Centers for Disease Control and Prevention (CDC), or fueled by irrational fear? What happened to compassion and help thy neighbor?” the Holland America Line president said in a statement.

“Already four guests have passed away and I fear other lives are at risk. As of March 30, 76 guests and 117 crew on Zaandam have influenza-like illness, including eight people who have tested positive for Covid-19,” it continued.

“The Covid-19 situation is one of the most urgent tests of our common humanity. To slam the door in the face of these people betrays our deepest human values.”

Passengers and crew on board in contact with the Guardian are increasingly concerned for their safety, which include 304 Americans, 228 British nationals and 116 Australians between both ships.