While addressing the media during a White House meeting with Texas Governor Greg Abbott, Trump said that he had had "very little contact, personal contact, with this gentleman", who is the President's personal military valet, adding that he had just undergone two coronavirus tests, one on Wednesday and another on Thursday, and the results were negative, reports Efe news.
However, Trump said he had ordered that people working at the White House be tested for the virus daily instead of weekly.
"So we test once a week, now we're going to go testing once a day," he said.
"But even when you test once a day, somebody could catch something."
Addressing Abbott as they chatted before reporters, Trump said: "I said yesterday, Governor, all people are warriors in this country. Right now we're all warriors."
On Thursday morning, the White House said in a statement that both Trump and Vice President Mike Pence had undergone virus tests after the valet had tested positive.
The personal valets are attached to the elite military units that serve at the White House and often work closely both with the president and the first lady, and thus concern has grown about whether Trump has been exposed to the sometimes deadly virus, which is still spreading rampantly in certain parts of the country.
This is not the first virus case to surface within the President's official residence with one of Pence's advisers testing positive for COVID-19 in March.
Although the rates of both new infections and deaths in New York state, the epicentre of the pandemic in the US, have been decelerating, the virus continues to spread throughout the rest of the country.
Concerned about the seriousness of the economic impact of the pandemic, Trump has been insisting on the need to resume business activities as soon as possible and has clashed on more than one occasion with medical experts who are recommending acting with greater prudence in confronting the huge public health crisis.
Trump said in his meeting with Abbott that Americans cannot remain confined for "years", with Texas being one of the states that has begun gradually easing movement restrictions.
On Thursday, unemployment application figures were released showing that in recent weeks more than 33 million people have lost their jobs in the US as economic activities have been severely curtailed.
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On the other hand, US media reported that the White House had urged a review of the federal guidelines for resuming economic activity after the draft prepared by the Centers for Disease Control and Prevention (CDC) was released.
One of the objections to the CDC guidelines put forward by the White House task force on the virus is that they did not distinguish between urban zones - which have had greater numbers of infections - and rural areas where, so far, there have been far fewer cases and deaths.
Trump said that there are counties in Texas that are barely affected by the virus, adding that the most important thing is to get the economy moving again.
The provisional death toll of more than 75,000 remains below the initial estimates of the White House, which projected in the best case scenario between 100,000 and 240,000 deaths from the virus, but it has exceeded the more optimistic initial figures Trump put forward of between 50,000 and 60,000 deaths.
Earlier this week, the President asserted that the total number of COVID-19 deaths in the US will be around 100,000 while simultaneously defending the decisions of many states to gradually ease quarantine measures, despite the fact that many of those states have not yet met the standards set forth in the original CDC guidelines for easing the restrictions.
Trump also admitted that easing the quarantine measures would certainly result in additional deaths.
The US currently accounts for the highest number of coronavirus cases and deaths in the world.
As of Friday, there were 1,256,972 cases in the country, while the death toll stood at 75,670, according to the Johns Hopkins University.