The order allows government agencies to delay the implementation of any parts of the Affordable Care Act – Barack Obama’s signature healthcare law – which could put a “fiscal burden” on families, states or healthcare providers.
It is the first step in Mr Trump’s plans to “promptly repeal” and replace Obamacare, a key promise made during his election campaign, but Republicans in Congress are yet to propose a replacement for the insurance programme.
Moments after signing the executive order, the President’s new defence secretary and homeland security secretary were sworn in by Vice President Mike Pence.
They are the first cabinet members to clear the hurdle of being approved by the Senate, which will begin confirming his other nominees on Monday.
In a statement, the President said: “I call on members of the Senate to fulfill their constitutional obligations and swiftly confirm the remainder of my highly qualified cabinet nominees, so that we can get to work on behalf of the American people without delay.”
During his election, Mr Trump had campaigned on a detailed 18-point plan of the things he would do on his first day in office.
But since then, he seems to have distanced himself from taking such a rapid-fire approach to implementing policies – especially when it comes to complicated issues which may involve negotiations with Congress or foreign leaders.
Within minutes of his inauguration as US President, Mr Trump’s administration announced plans to develop a “state-of-the-art” missile defence system to protect the US against attacks from Iran and North Korea.
The policy announcement comes a day after reports that Pyongyang was readying a test of an upgraded intercontinental ballistic missile prototype.
According to South Korean news agency Yonhap, news of the test appeared to have been intentionally leaked by North Korea to send a “strategic message” to Mr Trump.
In further measures, Mr Trump’s administration said it would reverse cutbacks to the defence budget and “submit a new budget to Congress outlining a plan to rebuild our military”.
It added: “We will provide our military leaders with the means to plan for our future defence needs.”
As Mr Trump’s pledges were published on the newly revamped White House website, references to climate change were deleted and replaced with the President’s “America First Energy Plan”.
The policy outlines intentions to scrap the “harmful and unnecessary” Climate Action Plan and Waters of the US rule brought in by Barack Obama.
It adds that the US has been “held back by burdensome regulations on our energy industry”.
Also detailed are plans to cut tax rates for workers and businesses, as well as a withdrawal from the Trans-Pacific Partnership trade agreement