6-7 minutes - Source: BBC
On Twitter, he cited "the attack from the invisible enemy", as he calls the virus, and the need to protect the jobs of Americans, but did not give details.
It was not clear what programmes might be affected and whether the president would be able to carry out the order.
Critics say the government is using the pandemic to crack down on immigration.
Mr Trump's announcement late on Monday comes as the White House argues the worst of the pandemic is over and the country can begin reopening. The restrictions on people's movement, implemented by many states to curb the spread of the virus, have paralysed parts of the economy.
Over the last four weeks, more than 20 million Americans have made jobless claims. That amounts to roughly as many jobs as employers had added over the previous decade.
The US has over 787,000 confirmed cases of Covid-19 and more than 42,000 deaths, according to a tally by Johns Hopkins University, which is tracking the pandemic globally.
It was not immediately clear who could be affected by Mr Trump's decision, and the White House has not commented. Last month, the US suspended almost all visa processing, including for immigrants, because of the pandemic.
The US has already agreed with both Canada and Mexico to extend border restrictions on non-essential travel until at least mid-May.
Travel has also been sharply restricted from hard-hit European countries and China, though people with temporary work visas, students and business travellers are exempted.
In recent weeks, emergency powers have been used to expel thousands of undocumented migrants on the US border with Mexico. The public health measure lets officials override immigration laws, expediting removal processes.
The reasons behind the moveDonald Trump's efforts at governing by social media should always be taken with a sizable grain of salt. His track record on following through on Twitter directives is decidedly mixed. The details of his temporary ban on all immigration, announced a few hours before midnight on Monday, will shed considerable light on the breadth - and legality - of his actions.
Still, it is no secret that the president, and several key advisers, have long viewed immigration not as a benefit to the nation, but as a drain. And the text of his tweet, that the move is necessary not only to protect the nation's health but also "the jobs of its great American citizens", only emphasises this.
There is little doubt the proposal, in whatever form it takes, will be vigorously opposed by pro-immigration groups, some business interests and the president's ideological adversaries. That is probably just fine with a man who loves drawing political battle lines and goading his opponents whenever possible.
Four years ago, the president campaigned on an aggressive anti-immigration platform, including a total, if temporary, ban on all Muslims entering the country. Now, with an uphill re-election fight looming, he has found a similarly combative measure to champion.
What's the latest in the US?Earlier on Monday, Democratic governors asked the White House to urge Americans to heed stay-at-home orders amid anti-lockdown protests stoked by the president.
Mr Trump has been accused of inciting insurrection after championing the demonstrators, while telling governors they were in charge.
He has expressed his support of the protesters in recent days, even as state governors say they are following White House guidance for safely reopening in phases.
A number of southern states in the US are in the process of easing virus-related restrictions.
South Carolina has allowed some retailers, including department stores, to re-open, while most businesses in Tennessee will re-open on 1 May.
Georgia's governor has said residents would be allowed to visit gyms, hairdressers and tattooists from Friday, followed by restaurants and cinemas on Monday, as long as those businesses operated within social distancing guidelines.
The Republican governors of all three states say social distancing measures will remain in place.
The WHO has previously warned about easing restrictions too early to avoid seeing a resurgence of infections.
Mr Trump - who faces an election in November - last week tweeted in all capital letters for several states to be liberated. At Sunday's coronavirus briefing, he said those protesting against their governors' social distancing measures were "great people".
"Their life was taken away from them," he said. "These people love our country, they want to get back to work."