His proclamation ordered agencies to ease the economic burden of the laws known as Obamacare.
In Friday's inaugural address he pledged to put "America first" and to end the "American carnage" of abandoned factories and rampant crime.
Later, about 200,000 people are due to join a Women's March in Washington.
Organisers say they want to highlight racial and gender equality and other issues perceived to be under threat from Mr Trump's administration.
Similar marches have taken place in Australia, New Zealand and in Asian cities, and many others are getting under way around the world.
BBC Washington correspondent Barbara Plett-Usher says Mr Trump has vowed to do what he can immediately using executive action, chalking up early victories before he has to turn to the grinding work of getting bills through Congress.
His team quickly overhauled the White House website to include his pledge to roll back Barack Obama's strategy on climate change.
Shortly after taking office as the 45th US president, Mr Trump sent his Cabinet nominations to the Senate.
He signed a waiver to allow retired General James Mattis to serve as defence secretary, even though he left the military less than the required seven years ago.
Gen Mattis, whose appointment has been approved by the Senate, was later sworn in by Vice-President Mike Pence.
Mr Pence also swore in John Kelly as head of Homeland Security.
The revamped White House website replaces Mr Obama's policies with Mr Trump's new agenda.
The new administration lists only six issues on the website - energy, foreign policy, jobs and growth, military, law enforcement and trade deals.
Critics point out that it makes no mention of civil rights, LGBT rights, healthcare or climate change.
One of Mr Trump's key election pledges was to repeal and replace President Barack Obama's Affordable Care Act.
Chief of Staff Reince Priebus said President Trump's executive order was for federal departments to "minimise the economic burden"' of the act, but he gave no details.
Mr Trump also signed a proclamation declaring a national day of patriotism.
Asked about his first day, which was capped by a dance with First Lady Melania to My Way, Mr Trump said "it was busy but good  - a beautiful day.''
In his inaugural address, Mr Trump, 70, struck a nationalist, protectionist tone.
"From this moment on, it's going to be America First. We will follow two simple rules: Buy American and hire American," he said.
Mr Trump accused Washington politicians of abandoning citizens to industrial decline and spiralling rates of crime.
"This American carnage stops right here and stops right now," he said.
"Every decision on trade, on taxes, on immigration, on foreign affairs, will be made to benefit American workers and American families."
Following the ceremony, some protesters took to the streets in Washington, smashing windows of businesses and denouncing capitalism and the new president.
Police in riot gear dispersed them using pepper spray.
More than 200 arrests were made and six officers were hurt. At least one vehicle was set on fire, police said.
Donald Trump has taken his first steps as president, signing an executive order which targets the signature health care reforms of his predecessor.