Trump, who has repeatedly threatened to punish countries if they don't spend enough on defense, said he would only agree if Poland is willing to pay the United States.
Poland has repeatedly requested a permanent USA military presence on its soil, offering up to $2 billion in funding for such a base.
In March, the United States and Poland said technical problems would delay completion of the Polish section of a USA missile defense shield by two years to 2020.
Currently, 3,000 US troops are deployed on a rotating basis in Poland, according to The Associated Press, a total which the North Atlantic Treaty Organisation ally is pressing the United States to increase. Warsaw is offering $2 billion to kick in toward the costs of a base.
Still, Trump's decision is surprising because he has talked about bringing USA troops home from across the world since he was on the campaign trail talking about America First.
Duda, for his part, came away confident that he had taken a major step toward lining up a permanent American military base in his country.
Donald Trump for additional $200 billion tariffs on China
If imposed, those tariffs would bring the total imports from China subject to penalties to more than $500 billion. The move came as both countries implemented tariffs this summer on $50 billion worth of goods from the other.
This gave President Donald Trump a smile.
"Looking at it from the standpoint of military protection": US President Donald Trump said.
He cited Russia's invasion of Georgia in 2008, its annexation of Crimea in 2014, and more recently, violations of ceasefire agreements in the provinces of Donetsk and Luhansk in Ukraine, as tangible "threat of aggression".
When a Polish reporter asked Trump about his own view of Russian behaviour in Europe, Trump did not hesitate to agree with Duda. Warsaw, long uneasy about a more aggressive Russia, has argued an Army brigade and associated support units stationed permanently in the country would serve as a more serious deterrent to Russian aggression. "I think Russian Federation has acted aggressively", he said.
"The United States commits to explore options for an increased USA military role in Poland and we will intensify our consultations to determine the concept's feasibility", the White House said in a statement later.
And the White House reinforced that judgment, saying a partnership between the U.S. and Poland "is critical in light of growing security challenges characterized by aggressive Russian behavior". "They respect force. They respect strength, as anyone does, and we have the greatest strength in the world, especially now".