But the order will not necessarily have any significant practical impact on the nation's health insurance system by the time Obamacare's next open enrollment season starts next month.
That's because of the time it takes to propose and take public comment on the potential changes.
And the order does not lift the Obamacare rule that most Americans have some form of health insurance for the year or face a tax penalty.
As a result of that omission, and other factors, it is not clear if the order will have a negative effect on enrollment in individual health plans sold on Obamacare plans that go into effect in 2018. Nor is it clear that enrollment in other health plans will increase significantly.
"I don't know that it accomplishes all that much" in the short-term, said Gary Claxton, a vice president at the Kaiser Family Foundation, a leading health-care policy research group, when asked about the order's impacts.
But Trump said, "Today is only the beginning."
"In the coming months we plan to take new measures to provide our people with even more relief and more freedom," Trump said, referring to other executive actions to reform rules related to the Affordable Care Act.
Claxton said if the administration ends up loosening enforcement of the Obamacare coverage mandate, "it could be disruptive, and it could happen very quickly."
Trump noted that in 2017, one-third of all counties in the United States had just one insurer offering Obamacare plans.
"Next year, it looks like nearly half of all counties in our country — think of that — one-half of our counties will have one insurer," Trump said.
Trump also pointed to "skyrocketing" health-care premium prices for Obamacare plans in a number of states in 2017 as evidence of the "Obamacare nightmare."
The order comes after months of failed efforts by Trump and Republican leaders to get Congress to pass legislation that would repeal and replace Obamacare.
Trump, who still wants such legislation to happen, on Thursday blamed congressional Democrats for universally opposing repeal-and-replace bills.
But the president also noted that it was a "small handful" of Republican senators whose opposition to those bills doomed them in recent months.
One of those senators was Rand Paul of Kentucky, who attended Thursday's signing session because he has advocated for making it easier for small businesses to form associations that can buy health insurance collectively. That idea is a key point in Trump's order.
The order directs the Labor Department to "consider expanding access to Association Health Plans" for American businesses, so small businesses can easier band together to offer health coverage. The order contemplates AHPs being formed across state lines.
The president said that by banding together, companies will be able to "buy affordable and competitive health coverage."
That, and allowing AHPs to buy coverage across state lines, will result in "staggering" competition for their business among insurers, Trump said.
"Insurers will be fighting to get every single person signed up," he said.
However, it is not clear if the Labor Department will end up allowing people who are not employed by companies in such AHPs to get health insurance coverage through them.
Obamacare advocates fear that if that were to be allowed, it could reduce the number of healthy people buying individual health plans on Obamacare exchanges. That, in turn, would lead to greater price hikes than have already been seen.
Advocates also worry that the AHP plans will not be as comprehensive in terms of covered benefits as Obamacare plans.
The order also directs several federal agencies to consider reversing an Obama administration directive that limited enrollment in short-term insurance plans to just three months.
Short-term health insurance currently does not satisfy Obamacare's coverage mandate, which means that someone enrolled in only those plans is subject to a tax penalty.
Claxton said that if the administration only ends up increasing the amount of time a person can be enrolled in a short-term insurance plan, "it would not have a big effect on undermining the [Obamacare] marketplaces," which sell more comprehensive, and more expensive, health coverage.
Claxton said that because individuals would still be subject to the penalty, there would not be a big influx of people into short-term plans and exodus out of Obamacare marketplace plans.
But "the issue would be, what comes next?" Claxton said.
If the administration liberalizes rules about the duration of short-term health plans, and then also makes it easier for people to get hardship exemptions from Obamacare's mandate, it could lead healthy people who don't need comprehensive benefits to sign up in large numbers for short-term coverage.
Dave Dillon, a fellow of the Society of Actuaries, said of Trump's order, "Overall, the proposal has potential to bring increased instability and volatility to the health insurance markets by separating the market into two smaller pools."
"Longer length short-term plans may further segment the market," Dillon said in emailed comments.
"The proposal offers more choice to consumers in terms of coverage options," Dillon said. "Healthier consumers will likely be able to enroll in plans with lower insurance rates, while more medically complex consumers may be subject to significant rate increases."
Trump's order also will direct federal agencies to consider making changes to rules around health-reimbursement arrangements, which allow employers to set aside tax-advantaged money that workers can use for out-of-pocket health costs.
And the order directs multiple agencies to review the level of competition among health-care providers and insurers nationally, with an eye toward identifying actions that could increase competition.
Officials said the administration is concerned about the large volume consolidation in the health-care sector since the adoption of the ACA, which they said has had the effect of increasing prices and potentially affecting the quality of health care.