Donald Trump has accused Democrats of “fearmongering” over the coronavirus outbreak, while claiming his decisions have “saved many lives” and asking drug companies to accelerate work on a vaccine.

The president made the claim on Twitter on Monday morning, continuing a spat which has seen him accused of politicising the health crisis as America struggles to deal with the outbreak on US soil.

Two people have died from the coronavirus in the US and new cases were reported over the weekend in Washington state, New York, Florida, Rhode Island and Illinois. There are about 75 cases of the respiratory illness recorded in the US.

“The country’s doing very well, our professionals are doing an incredible job,” Trump told journalists at the White House on Monday. “We’re also working with other countries to help them because they really have a fear of the unknown.”

“Also I’m meeting with the pharmaceutical companies later on this afternoon, we have a big meeting with the biggest companies. We’re talking about a vaccine, maybe a cure, it’s possible, we’ll see about that … We’ve asked them to accelerate whatever they’re doing in terms of a vaccine.”

We’re talking about a vaccine, maybe a cure, it’s possible, we’ll see about that Donald Trump

Most who contract coronavirus survive but it can develop into pneumonia-like illness and the elderly and those with chronic health problems are especially at risk. According to the World Health Organization, more than 87,000 cases have been confirmed worldwide and nearly 3,000 deaths. Most are in China but the illness is spreading.

International financial markets have plummeted and travel, business and sporting events have been increasingly affected.

The Trump administration announced new measures to contain the outbreak on Saturday and sought to calm fears with appearances across the US media by figures including officials of the Centers for Disease Control and Prevention and the US health secretary, Alex Azar.

But Mike Pence, in charge of the White House task force, caused controversy when he refused to condemn remarks by Trump supporters including Donald Trump Jr which claimed Democrats were politicising the outbreak.

Appearing on Fox News on Friday, Trump Jr said: “For them to try to take a pandemic and seemingly hope that it comes here and kills millions of people so that they could end Donald Trump’s streak of winning is a new level of sickness.”

The vice-president told NBC on Sunday: “When you see voices on our side pushing back on outrageous and irresponsible rhetoric on the other side, I think that’s important, and I think it’s justified.”

In his Monday tweet, the president returned to the offensive.

“I was criticized by the Democrats when I closed the Country down to China many weeks ahead of what almost everyone recommended,” he wrote. “Saved many lives. [Democrats] were working the Impeachment Hoax. They didn’t have a clue! Now they are fear mongering. Be calm & vigilant!”

Trump did not close travel from China but did impose controls. Several airlines have suspended flights to and from China.

Media coverage of the outbreak has been criticized but Trump has also attracted flak for placing himself front and center of a White House response that has been reported to be chaotic and uncoordinated. Trump has also been criticized for seeming to play down the seriousness of the outbreak.

On Sunday, Joe Biden, who won the South Carolina primary the night before, tweeted: “Only Donald Trump could make the coronavirus about him. This president is dangerous.”

Trump’s use of the word “hoax” revisited remarks at a rally in South Carolina on Friday night. At a White House press briefing on Saturday, Trump insisted he used it in reference to the Democrats’ behaviour around the outbreak, rather than the outbreak itself.

In the Oval Office on Monday, Trump told reporters he did not think it was unwise to continue to hold large public gatherings as coronavirus spreads.

His scheduled event in North Carolina on Monday “was set up a long time ago and others are,” he said. “You could ask that to the Democrats … They’re all having rallies, that’s what they’re doing, they’re campaigning.

“I think it’s very safe.”