A senior member of Donald Trump's administration has admitted that plans for disembarking a cruise ship on which 21 people are known to have the coronavirus are not "fully formulated".

Ben Carson, the housing secretary, told ABC's This Week that plans on how to deal with the Grand Princess were yet to be completed.

The ship, which has more than 3,500 people on board, is due to dock in Oakland, California on Monday after being anchored off San Francisco for several days.

So far 19 employees and two passengers have tested positive for Covid-19. Another 24 people tested negative and one case was inconclusive. There are about 3,500 passengers on board.

On Sunday it was announced that when passengers disembark in Oakland, those who need treatment will receive it at healthcare facilities in California while state residents "will go to a federally operated isolation facility" for testing and isolation. Non-California residents will be tested elsewhere – in Texas or Georgia, where they will be quarantined for 14 days – and crew will remain on the ship.

Dr Carson, a former neurosurgeon, was asked by presenter George Stephanopoulos what the plan was for dealing with passengers and crew.

He said: "As you know the vice-president met with the CEOs of the major cruise ship companies yesterday, and they are coming up with a plan within 72 hours of that meeting."

Dr Carson said the plan would be in place by the time the ship docks, but added: "I don't want to preview the plan right now."

Stephanopoulos asked: "Shouldn't you be able to do that?"

The housing secretary replied: "I think it needs to come from a solitary source. We shouldn't have 16 people saying what the plan is – particularly when it hasn't been fully formulated."

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The presenter responded: "OK, well you're the president's representative this morning but we'll move on."

On Friday, Mr Trump said he wanted to keep passengers and crew on board so that US cases would not "double".

He said: "They would like to have the people come off. I'd rather have the people stay. But I'd go with them. I told them to make the final decision. I would rather – because I like the numbers being where they are. I don't need to have the numbers double because of one ship that wasn't our fault."

California governor Gavin Newsom said the ship would be docking in Oakland on Monday after various locations had been considered, but said an exact time was yet to be determined, depending on currents and the state of preparations. Medical staff will be sent onboard to screen passengers. Foreign nationals on the ship are expected to be flown out of the country on private chartered flights.

He said that 114 people in the state had tested positive and one had died – a man who had previously been on the Grand Princess. Some 1,540 California residents who were on the previous cruise are being monitored and 12 have been confirmed as having Covid-19.

The president has angrily rejected persistent claims that his administration has failed to get to grips with the threat of Covid-19, which has now infected more than 400 people in the United States and claimed 19 lives.

He sent a Sunday morning tweet reading: "We have a perfectly coordinated and fine tuned plan at the White House for our attack on CoronaVirus. We moved VERY early to close borders to certain areas, which was a Godsend. V.P. is doing a great job. The Fake News Media is doing everything possible to make us look bad. Sad!"

His top expert on coronavirus, Anthony Fauci, director of the National Institute of Allergy and Infectious Diseases, has warned elderly people with underlying health conditions to restrict their travel and avoid large gatherings.

He told NBC's Meet the Press: "If you are an elderly person with an underlying condition, if you get infected, the risk of getting into trouble is considerable. So it's our responsibility to protect the vulnerable.

"When I say protect, I mean right now. Not wait until things get worse. Say no large crowds, no long trips.

"And above all, don't get on a cruise ship."

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On Sunday Oregon became the latest US state to declare a state of emergency over the virus. Governor Kate Brown announced the move, which should make more funding available to deal with the threat, after seven more cases were confirmed in the state on Saturday night, bringing the total to 14.