The entry for immigrants will be suspected, according to the proclamation, "unless the alien possesses the financial resources to pay for reasonably foreseeable medical costs".
In each year over the last decade, health providers have covered over $35 billion in expenses for uninsured patients, or about $7 million on average for every hospital in the U.S., the White House said.
He has pushed wide-ranging immigration law reforms, while tasking authorities with carrying out mass deportations of people in the United States illegally.
This will be effective from November 3.Trump made cracking down on immigration a key part of his 2016 presidential campaign platform.
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However, the order passed by the White House claimed that it will not affect an individual's eligibility for asylum or refugee status. That new rule is set to take effect this month, although it is facing legal challenges.
"Immigrants who enter this country should not further saddle our healthcare system, and subsequently American taxpayers, with higher costs".
Trump said he is taking the action to "protect the availability of health care benefits for Americans", and said "taxpayers bear substantial cost" in paying for medical expenses of people who lack health insurance.
The State Department program allows foreign citizens to visit the United States for up to 90 days without a visa.
"If Poland is designated as a Visa Waiver Program country, its nationals would be authorized for visa-free travel to the United States for business and tourism", the White House said.
The bilateral relationship between the United States and Poland has never been stronger, and this would serve as a remarkable accomplishment for both countries.
The Trump administration is trying to move away from a family-based immigration system and into a merit-based system, and Friday's proclamation is another effort to limit immigrant access to public programs.