Donald Trump picked fights with Democrats on Tuesday even as he called for them to “keep politics out” of the battle against what he called, in a return to nationalist rhetoric, “the Chinese virus”.

As the White House prepares a massive stimulus package to counter the effect of the Covid-19 outbreak, the president gave an upbeat assessment of the economy, seen as critical to his political future, promising it would “pop” again soon.

“We’re going to win,” he vowed.

That this crisis is taking place in an election year is impossible to ignore.

“I watched the debate – not too exciting,” Trump said of last Sunday’s meeting between Joe Biden and Bernie Sanders. “But what they said about me – and we’ve done a great job – when you talk about not being bipartisan, what they said about me.”

He accused the Obama administration, in which Biden was vice-president, of making “terrible” and “horrific” mistakes in handling a swine flu outbreak in 2009.

“Seventeen thousand people died,” Trump told reporters at a coronavirus taskforce briefing. In fact the official death toll in the US was 12,469.

“They shouldn’t be criticising because we’ve done a fantastic job,” Trump added, before airing a familiar grievance.

“The only thing we haven’t done well is to get good press. We’ve done a fantastic job but it hasn’t been appreciated.

“Even the closing down of the borders, which had never been done, and not only did we close them but we closed them early. The press doesn’t like writing about it. So we’ve done a poor job on press relationships and I guess I don’t know who to blame for that. I don’t know, maybe I can blame ourselves for that. I will blame ourselves.”

In a rare Oval Office address last week, Trump urged unity. But almost every day since he has attacked Obama, Biden or Democratic governors. He began Tuesday by going after governors Andrew Cuomo of New York and Gretchen Whitmer of Michigan.

He tweeted: “Cuomo wants ‘all states to be treated the same.’ But all states aren’t the same. Some are being hit hard by the Chinese Virus, some are being hit practically not at all. New York is a very big ‘hotspot’, West Virginia has, thus far, zero cases.”

Trump added: “Andrew, keep politics out of it …”

New York is now among the worst affected by the coronavirus. But at a press conference in Albany, Cuomo struck a conciliatory tone: “I said to the president, who is a New Yorker … ‘I put my hand out in partnership. I want to work together 100%. I want your help. I need your help.

“I think the president was 100% sincere in saying he wanted to work together in partnership, in a spirt of cooperation. The actions he has taken evidence that. His team are on it.”

Trump also attacked Whitmer, seen as a potential running mate for Biden.

“Failing Michigan governor must work harder and be much more proactive,” he wrote. “We are pushing her to get the job done. I stand with Michigan!”

Whitmer shot back, seeking “swift and clear guidance, tests, personal protective equipment, and resources”. She went on to list measures taken in her state, a key election battleground.

At the White House, Trump insisted: “I only do that when I have to respond. I watched her [Whitmer] on television. She said something that was false and therefore I did do that and I will continue to do that.

“If they’re not going to play fair, because you know, they have the media on their side. I don’t. I just have me. And if they’re not going to play fair, I’m going to do that. If they are going to play fair, there’s going to be nobody better than Donald Trump in terms of bipartisanship.”

Trump also faced criticism for his use of the phrase “Chinese virus”. Congressman Ted Lieu tweeted: “There’s a difference between saying a virus came from China versus calling it a Chinese virus. Asian Americans have already been assaulted because of this type of rhetoric.”

Asked by the Guardian if he intended to continue using the phrase, Trump replied: “China was putting out information, which was false, that our military gave this to them. That was false and rather than having an argument I said I have to call it where it came from. It did come from China so I think it’s a very accurate term.”

More than a month ago, the World Health Organization director general, Tedros Adhanom Ghebreyesus, said the novel strain of the coronavirus had an official name, Covid-19, which should “prevent the use of other names that can be inaccurate or stigmatizing”.

A robust economy had been seen as Trump’s strongest suit for re-election. Now he faces recession. Airlines are said to face a bigger crisis than after 9/11.

Trump insisted: “If we do this right, our country can be rolling again pretty quickly. We have to fight that invisible enemy. I guess, unknown – but we’re getting to know it a lot better.”

He added: “The best thing we can do is get rid of the virus. Once that’s gone, it’s going to pop back like nobody’s ever seen before, that’s my opinion … I think our economy will come back really rapidly. One day we’ll be standing possibly up here, we’ll say, ‘Well, we won.’ Sure as you’re sitting here, we’re going to say that. We’re going to win.”

Trump has claimed credit for banning travel from China early on but faced condemnation for not moving faster on widespread testing. Despite a long list of public statements in which he downplayed the threat, on Tuesday he made a startling claim: “I’ve always known this is a real – this is a pandemic.

“I felt it was a pandemic long before it was called a pandemic.”