Donald Trump said he wanted to get Americans back to work as the US Congress agreed to a stimulus bill worth almost $2 trillion.
The FTSE 100 rose by more than 9 per cent on Tuesday, its second best day on record behind a bounce in November 2008, while the Dow Jones in America was initially up 8 per cent.
"Our country is not built to shut down,” Mr Trump said, adding he would consider changing guidance that tells people to work at home and not eat in restaurants next week.
He also warned that more people could die if the economy crashes and jobs are lost than from the pandemic, citing concerns over suicides.
Mr Trump, pushed later in a White House briefing on why he picked Easter as the target for lifting restrictions, said: "I just thought it was a beautiful time".
Such talk has alarmed some health experts who fear easing nationwide restrictions too early to protect the economy could inadvertently help spread the virus.
America was approaching its 50,000th confirmed coronavirus case last night, up from around 6,000 a week ago. There have been around 600 deaths.
The World Health Organisation [WHO] has warned that the United States could become the outbreak’s new epicentre.
Hours after Mr Trump spoke, Democrat and Republican politicians agreed terms on the largest emergency economic bill in US history.
The unprecedented economic rescue package would give direct payments to most Americans, expand unemployment benefits and provide a $367 billion programme for small businesses to keep making payroll while workers are forced to stay home.
One of the last issues to close concerned $500 billion for guaranteed, subsidised loans to larger industries, including a fight over how generous to be with the airlines. Hospitals would get significant help as well.
"After days of intense discussions, the Senate has reached a bipartisan agreement on a historic relief package for this pandemic," said Majority Leader Mitch McConnell, a key negotiator. "It will rush new resources onto the front lines of our nation's health care fight. And it will inject trillions of dollars of cash into the economy as fast as possible to help Americans workers, families, small businesses and industries make it through this disruption and emerge on the other side ready to soar."
Meanwhile the White House coronavirus taskforce urged anyone who has left New York city recently to self-quarantine for 14 days, given the high number of cases there.
Mr Trump’s change in rhetoric and the deal in Congress - appeared to influence investor thinking as stock markets jumped after historic drops.
Mr Trump has been voicing concern in the last 48 hours that the economy is suffering too much from restrictions designed to stop the spread of coronavirus.
He echoed that in a Fox News interview on Tuesday, saying: “Our people are full of vim and vigour and energy, they don’t want to be locked in a house or an apartment or some space.”
The president added: "We lose thousands and thousands of people a year to the flu. We don’t turn the country off."
Mr Trump argued that if the economy was forced into a “massive" recession there could be “thousands" of suicides as people despair over lost jobs and ruined businesses.
He insisted it was possible to both stop the virus’s spread and allow some people to return to their jobs, saying: “We can socially distance ourselves and we can go to work.”
The president said next week when the 15-day initial period ends on his nationwide guidelines, which include urging people not to gather in groups of more than 10 and work from home, he will decide whether to continue with them.
Mr Trump did not indicate exactly how the guidance could change or when but said: “I would love to have the country opened up and just raring to go by Easter.”
Easter Sunday is on April 12, just 18 days away. Andrew Cuomo, the New York governor - the worst affected state in America - was among those who pushed back on Mr Trump’s suggestion that restrictions should be lifted.
“My mother is not expendable. Your mother is not expendable. We will not put a dollar figure on human life,” Mr Cuomo tweeted.
“We can have a public health strategy that is consistent with an economic one. No one should be talking about social darwinism for the sake of the stock market.”
Margaret Harris, the WHO spokeswoman, noted in a briefing on Tuesday that 85 per cent of new cases over the proceeding 24 hours were from the United States and Europe.
Asked if the US could become the new epicentre, Ms Harris said: "We are now seeing a very large acceleration in cases in the US. So it does have that potential.”
Dame Karen Pierce flew into Washington DC on Thursday to take up the post but arrived from Britain, meaning she was impacted by restrictions on travellers from Europe.
She was screened for the virus upon arrival at the airport and, in line with the new rules, is spending 14 days in effective self-quarantine in the British ambassador's residence.
It means Dame Karen is currently unable to meet face-to-face with US cabinet members and congressmen or even gather in person with her own advisers due to the restrictions.